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Xiang, Communications in Partial Differential Equations 46 (2021) 1058–1091.","bibtex":"@article{Wang_Winkler_Xiang_2021, title={Local energy estimates and global solvability in a  threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary.}, volume={46}, journal={Communications in Partial Differential Equations}, author={Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}, year={2021}, pages={1058–1091} }","apa":"Wang, Y., Winkler, M., &#38; Xiang, Z. (2021). Local energy estimates and global solvability in a  threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary. <i>Communications in Partial Differential Equations</i>, <i>46</i>, 1058–1091.","mla":"Wang, Yulan, et al. “Local Energy Estimates and Global Solvability in a  Threee-Dimensional Chemotaxis-Fluid System with Prescribed Signal on the Boundary.” <i>Communications in Partial Differential Equations</i>, vol. 46, 2021, pp. 1058–91.","ieee":"Y. Wang, M. Winkler, and Z. Xiang, “Local energy estimates and global solvability in a  threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary.,” <i>Communications in Partial Differential Equations</i>, vol. 46, pp. 1058–1091, 2021."},"publication":"Communications in Partial Differential Equations","date_created":"2023-01-09T18:00:41Z","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"type":"journal_article","author":[{"first_name":"Yulan","last_name":"Wang","full_name":"Wang, Yulan"},{"id":"31496","first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"},{"full_name":"Xiang, Zhaoyin","last_name":"Xiang","first_name":"Zhaoyin"}],"year":"2021","title":"Local energy estimates and global solvability in a  threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary.","status":"public","intvolume":"        46","date_updated":"2023-02-01T10:25:34Z","language":[{"iso":"eng"}],"_id":"35610","page":"1058-1091","volume":46,"user_id":"15645"},{"citation":{"chicago":"Wang, Yulan, Michael Winkler, and Zhaoyin Xiang. “Global Solvability in a Threee-Dimensional Keller-Segel.Stokes System Involving Arbitrary Superlinear Logistic Degradation.” <i>Advances in Nonlinear Analysis</i> 10 (2021): 707–31.","short":"Y. Wang, M. Winkler, Z. Xiang, Advances in Nonlinear Analysis 10 (2021) 707–731.","apa":"Wang, Y., Winkler, M., &#38; Xiang, Z. (2021). Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation. <i>Advances in Nonlinear Analysis</i>, <i>10</i>, 707–731.","ieee":"Y. Wang, M. Winkler, and Z. Xiang, “Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation,” <i>Advances in Nonlinear Analysis</i>, vol. 10, pp. 707–731, 2021.","ama":"Wang Y, Winkler M, Xiang Z. Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation. <i>Advances in Nonlinear Analysis</i>. 2021;10:707-731.","bibtex":"@article{Wang_Winkler_Xiang_2021, title={Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation}, volume={10}, journal={Advances in Nonlinear Analysis}, author={Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}, year={2021}, pages={707–731} }","mla":"Wang, Yulan, et al. “Global Solvability in a Threee-Dimensional Keller-Segel.Stokes System Involving Arbitrary Superlinear Logistic Degradation.” <i>Advances in Nonlinear Analysis</i>, vol. 10, 2021, pp. 707–31."},"publication":"Advances in Nonlinear Analysis","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"type":"journal_article","date_created":"2023-01-09T18:03:45Z","intvolume":"        10","date_updated":"2023-02-01T10:27:17Z","author":[{"first_name":"Yulan","last_name":"Wang","full_name":"Wang, Yulan"},{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"},{"last_name":"Xiang","first_name":"Zhaoyin","full_name":"Xiang, Zhaoyin"}],"year":"2021","status":"public","title":"Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation","volume":10,"user_id":"15645","_id":"35611","language":[{"iso":"eng"}],"page":"707-731"},{"status":"public","publisher":"Springer Science and Business Media LLC","_id":"34673","user_id":"23686","volume":72,"citation":{"bibtex":"@article{Black_Fuest_Lankeit_2021, title={Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems}, volume={72}, DOI={<a href=\"https://doi.org/10.1007/s00033-021-01524-8\">10.1007/s00033-021-01524-8</a>}, number={396}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer Science and Business Media LLC}, author={Black, Tobias and Fuest, Mario and Lankeit, Johannes}, year={2021} }","ama":"Black T, Fuest M, Lankeit J. Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems. <i>Zeitschrift für angewandte Mathematik und Physik</i>. 2021;72(3). doi:<a href=\"https://doi.org/10.1007/s00033-021-01524-8\">10.1007/s00033-021-01524-8</a>","mla":"Black, Tobias, et al. “Relaxed Parameter Conditions for Chemotactic Collapse in Logistic-Type Parabolic–Elliptic Keller–Segel Systems.” <i>Zeitschrift Für Angewandte Mathematik Und Physik</i>, vol. 72, no. 3, 96, Springer Science and Business Media LLC, 2021, doi:<a href=\"https://doi.org/10.1007/s00033-021-01524-8\">10.1007/s00033-021-01524-8</a>.","chicago":"Black, Tobias, Mario Fuest, and Johannes Lankeit. “Relaxed Parameter Conditions for Chemotactic Collapse in Logistic-Type Parabolic–Elliptic Keller–Segel Systems.” <i>Zeitschrift Für Angewandte Mathematik Und Physik</i> 72, no. 3 (2021). <a href=\"https://doi.org/10.1007/s00033-021-01524-8\">https://doi.org/10.1007/s00033-021-01524-8</a>.","short":"T. Black, M. Fuest, J. Lankeit, Zeitschrift Für Angewandte Mathematik Und Physik 72 (2021).","ieee":"T. Black, M. Fuest, and J. Lankeit, “Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems,” <i>Zeitschrift für angewandte Mathematik und Physik</i>, vol. 72, no. 3, Art. no. 96, 2021, doi: <a href=\"https://doi.org/10.1007/s00033-021-01524-8\">10.1007/s00033-021-01524-8</a>.","apa":"Black, T., Fuest, M., &#38; Lankeit, J. (2021). Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems. <i>Zeitschrift Für Angewandte Mathematik Und Physik</i>, <i>72</i>(3), Article 96. <a href=\"https://doi.org/10.1007/s00033-021-01524-8\">https://doi.org/10.1007/s00033-021-01524-8</a>"},"year":"2021","title":"Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems","publication_identifier":{"issn":["0044-2275","1420-9039"]},"author":[{"full_name":"Black, Tobias","first_name":"Tobias","orcid":"0000-0001-9963-0800","last_name":"Black","id":"23686"},{"full_name":"Fuest, Mario","first_name":"Mario","last_name":"Fuest"},{"last_name":"Lankeit","first_name":"Johannes","full_name":"Lankeit, Johannes"}],"date_updated":"2023-07-10T11:39:23Z","publication_status":"published","intvolume":"        72","article_number":"96","language":[{"iso":"eng"}],"doi":"10.1007/s00033-021-01524-8","issue":"3","publication":"Zeitschrift für angewandte Mathematik und Physik","date_created":"2022-12-21T09:48:36Z","type":"journal_article","keyword":["Applied Mathematics","General Physics and Astronomy","General Mathematics"],"department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}]},{"citation":{"chicago":"Black, Tobias, and Chunyan Wu. “Prescribed Signal Concentration on the Boundary: Weak Solvability in a Chemotaxis-Stokes System with Proliferation.” <i>Zeitschrift Für Angewandte Mathematik Und Physik</i> 72, no. 4 (2021). <a href=\"https://doi.org/10.1007/s00033-021-01565-z\">https://doi.org/10.1007/s00033-021-01565-z</a>.","short":"T. Black, C. Wu, Zeitschrift Für Angewandte Mathematik Und Physik 72 (2021).","apa":"Black, T., &#38; Wu, C. (2021). Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation. <i>Zeitschrift Für Angewandte Mathematik Und Physik</i>, <i>72</i>(4), Article 135. <a href=\"https://doi.org/10.1007/s00033-021-01565-z\">https://doi.org/10.1007/s00033-021-01565-z</a>","ieee":"T. Black and C. Wu, “Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation,” <i>Zeitschrift für angewandte Mathematik und Physik</i>, vol. 72, no. 4, Art. no. 135, 2021, doi: <a href=\"https://doi.org/10.1007/s00033-021-01565-z\">10.1007/s00033-021-01565-z</a>.","ama":"Black T, Wu C. Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation. <i>Zeitschrift für angewandte Mathematik und Physik</i>. 2021;72(4). doi:<a href=\"https://doi.org/10.1007/s00033-021-01565-z\">10.1007/s00033-021-01565-z</a>","bibtex":"@article{Black_Wu_2021, title={Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation}, volume={72}, DOI={<a href=\"https://doi.org/10.1007/s00033-021-01565-z\">10.1007/s00033-021-01565-z</a>}, number={4135}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer Science and Business Media LLC}, author={Black, Tobias and Wu, Chunyan}, year={2021} }","mla":"Black, Tobias, and Chunyan Wu. “Prescribed Signal Concentration on the Boundary: Weak Solvability in a Chemotaxis-Stokes System with Proliferation.” <i>Zeitschrift Für Angewandte Mathematik Und Physik</i>, vol. 72, no. 4, 135, Springer Science and Business Media LLC, 2021, doi:<a href=\"https://doi.org/10.1007/s00033-021-01565-z\">10.1007/s00033-021-01565-z</a>."},"status":"public","publisher":"Springer Science and Business Media LLC","_id":"34675","volume":72,"user_id":"23686","publication":"Zeitschrift für angewandte Mathematik und Physik","issue":"4","date_created":"2022-12-21T09:48:45Z","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"keyword":["Applied Mathematics","General Physics and Astronomy","General Mathematics"],"type":"journal_article","publication_identifier":{"issn":["0044-2275","1420-9039"]},"author":[{"full_name":"Black, Tobias","orcid":"0000-0001-9963-0800","first_name":"Tobias","last_name":"Black","id":"23686"},{"last_name":"Wu","first_name":"Chunyan","full_name":"Wu, Chunyan"}],"title":"Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation","year":"2021","intvolume":"        72","publication_status":"published","date_updated":"2023-07-10T11:39:30Z","language":[{"iso":"eng"}],"article_number":"135","doi":"10.1007/s00033-021-01565-z"},{"date_updated":"2026-02-26T21:15:28Z","author":[{"first_name":"Natalie","last_name":"Nikitin","full_name":"Nikitin, Natalie"}],"status":"public","year":"2021","title":"Regularity properties of infinite-dimensional Lie groups and exponential laws","user_id":"178","_id":"64765","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://nbn-resolving.org/urn:nbn:de:hbz:466:2-39133"}],"citation":{"ama":"Nikitin N. <i>Regularity Properties of Infinite-Dimensional Lie Groups and Exponential Laws</i>.; 2021.","bibtex":"@book{Nikitin_2021, title={Regularity properties of infinite-dimensional Lie groups and exponential laws}, author={Nikitin, Natalie}, year={2021} }","mla":"Nikitin, Natalie. <i>Regularity Properties of Infinite-Dimensional Lie Groups and Exponential Laws</i>. 2021.","short":"N. Nikitin, Regularity Properties of Infinite-Dimensional Lie Groups and Exponential Laws, 2021.","chicago":"Nikitin, Natalie. <i>Regularity Properties of Infinite-Dimensional Lie Groups and Exponential Laws</i>, 2021.","apa":"Nikitin, N. (2021). <i>Regularity properties of infinite-dimensional Lie groups and exponential laws</i>.","ieee":"N. Nikitin, <i>Regularity properties of infinite-dimensional Lie groups and exponential laws</i>. 2021."},"supervisor":[{"id":"178","last_name":"Glöckner","first_name":"Helge","full_name":"Glöckner, Helge"}],"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"oa":"1","type":"dissertation","date_created":"2026-02-26T21:15:13Z"},{"date_created":"2022-12-21T19:17:28Z","keyword":["22D05","22A05","20E18"],"type":"journal_article","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"publication":"Journal für die reine und angewandte Mathematik","language":[{"iso":"eng"}],"doi":"10.1515/crelle-2021-0050","title":"Locally pro-p contraction groups are nilpotent","year":"2021","publication_identifier":{"issn":["0075-4102"]},"author":[{"id":"178","full_name":"Glöckner, Helge","first_name":"Helge","last_name":"Glöckner"},{"last_name":"Willis","first_name":"George A.","full_name":"Willis, George A."}],"date_updated":"2026-02-27T08:34:58Z","article_type":"original","intvolume":"       781","citation":{"chicago":"Glöckner, Helge, and George A. Willis. “Locally Pro-p Contraction Groups Are Nilpotent.” <i>Journal Für Die Reine Und Angewandte Mathematik</i> 781 (2021): 85–103. <a href=\"https://doi.org/10.1515/crelle-2021-0050\">https://doi.org/10.1515/crelle-2021-0050</a>.","short":"H. Glöckner, G.A. Willis, Journal Für Die Reine Und Angewandte Mathematik 781 (2021) 85–103.","ama":"Glöckner H, Willis GA. Locally pro-p contraction groups are nilpotent. <i>Journal für die reine und angewandte Mathematik</i>. 2021;781:85–103. doi:<a href=\"https://doi.org/10.1515/crelle-2021-0050\">10.1515/crelle-2021-0050</a>","bibtex":"@article{Glöckner_Willis_2021, title={Locally pro-p contraction groups are nilpotent}, volume={781}, DOI={<a href=\"https://doi.org/10.1515/crelle-2021-0050\">10.1515/crelle-2021-0050</a>}, journal={Journal für die reine und angewandte Mathematik}, author={Glöckner, Helge and Willis, George A.}, year={2021}, pages={85–103} }","mla":"Glöckner, Helge, and George A. Willis. “Locally Pro-p Contraction Groups Are Nilpotent.” <i>Journal Für Die Reine Und Angewandte Mathematik</i>, vol. 781, 2021, pp. 85–103, doi:<a href=\"https://doi.org/10.1515/crelle-2021-0050\">10.1515/crelle-2021-0050</a>.","apa":"Glöckner, H., &#38; Willis, G. A. (2021). Locally pro-p contraction groups are nilpotent. <i>Journal Für Die Reine Und Angewandte Mathematik</i>, <i>781</i>, 85–103. <a href=\"https://doi.org/10.1515/crelle-2021-0050\">https://doi.org/10.1515/crelle-2021-0050</a>","ieee":"H. Glöckner and G. A. Willis, “Locally pro-p contraction groups are nilpotent,” <i>Journal für die reine und angewandte Mathematik</i>, vol. 781, pp. 85–103, 2021, doi: <a href=\"https://doi.org/10.1515/crelle-2021-0050\">10.1515/crelle-2021-0050</a>."},"quality_controlled":"1","page":"85–103","_id":"34790","user_id":"178","volume":781,"status":"public"},{"intvolume":"        56","article_type":"original","date_updated":"2022-12-21T19:15:59Z","author":[{"first_name":"Habib","last_name":"Amiri","full_name":"Amiri, Habib"},{"full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge","id":"178"},{"full_name":"Schmeding, Alexander","first_name":"Alexander","last_name":"Schmeding"}],"publication_identifier":{"issn":["0044-8753"]},"title":"Lie groupoids of mappings taking values in a Lie groupoid","year":"2020","doi":"10.5817/AM2020-5-307","language":[{"iso":"eng"}],"publication":"Archivum Mathematicum","issue":"5","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"keyword":["22A22","22E65","22E67","46T10","47H30","58D15","58H05"],"type":"journal_article","date_created":"2022-12-21T19:13:24Z","status":"public","volume":56,"user_id":"178","_id":"34789","page":"307–356","quality_controlled":"1","citation":{"ama":"Amiri H, Glöckner H, Schmeding A. Lie groupoids of mappings taking values in a Lie groupoid. <i>Archivum Mathematicum</i>. 2020;56(5):307–356. doi:<a href=\"https://doi.org/10.5817/AM2020-5-307\">10.5817/AM2020-5-307</a>","bibtex":"@article{Amiri_Glöckner_Schmeding_2020, title={Lie groupoids of mappings taking values in a Lie groupoid}, volume={56}, DOI={<a href=\"https://doi.org/10.5817/AM2020-5-307\">10.5817/AM2020-5-307</a>}, number={5}, journal={Archivum Mathematicum}, author={Amiri, Habib and Glöckner, Helge and Schmeding, Alexander}, year={2020}, pages={307–356} }","mla":"Amiri, Habib, et al. “Lie Groupoids of Mappings Taking Values in a Lie Groupoid.” <i>Archivum Mathematicum</i>, vol. 56, no. 5, 2020, pp. 307–356, doi:<a href=\"https://doi.org/10.5817/AM2020-5-307\">10.5817/AM2020-5-307</a>.","short":"H. Amiri, H. Glöckner, A. Schmeding, Archivum Mathematicum 56 (2020) 307–356.","chicago":"Amiri, Habib, Helge Glöckner, and Alexander Schmeding. “Lie Groupoids of Mappings Taking Values in a Lie Groupoid.” <i>Archivum Mathematicum</i> 56, no. 5 (2020): 307–356. <a href=\"https://doi.org/10.5817/AM2020-5-307\">https://doi.org/10.5817/AM2020-5-307</a>.","apa":"Amiri, H., Glöckner, H., &#38; Schmeding, A. (2020). Lie groupoids of mappings taking values in a Lie groupoid. <i>Archivum Mathematicum</i>, <i>56</i>(5), 307–356. <a href=\"https://doi.org/10.5817/AM2020-5-307\">https://doi.org/10.5817/AM2020-5-307</a>","ieee":"H. Amiri, H. Glöckner, and A. Schmeding, “Lie groupoids of mappings taking values in a Lie groupoid,” <i>Archivum Mathematicum</i>, vol. 56, no. 5, pp. 307–356, 2020, doi: <a href=\"https://doi.org/10.5817/AM2020-5-307\">10.5817/AM2020-5-307</a>."}},{"keyword":["54B10","54D45","54D50"],"type":"journal_article","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"date_created":"2022-12-21T19:06:45Z","quality_controlled":"1","publication":"Topology Proceedings","citation":{"mla":"Glöckner, Helge, and Niku Masbough. “Products of Regular Locally Compact Spaces Are K_R-Spaces.” <i>Topology Proceedings</i>, vol. 55, 2020, pp. 35–38.","bibtex":"@article{Glöckner_Masbough_2020, title={Products of regular locally compact spaces are k_R-spaces}, volume={55}, journal={Topology Proceedings}, author={Glöckner, Helge and Masbough, Niku}, year={2020}, pages={35–38} }","ama":"Glöckner H, Masbough N. Products of regular locally compact spaces are k_R-spaces. <i>Topology Proceedings</i>. 2020;55:35–38.","ieee":"H. Glöckner and N. Masbough, “Products of regular locally compact spaces are k_R-spaces,” <i>Topology Proceedings</i>, vol. 55, pp. 35–38, 2020.","apa":"Glöckner, H., &#38; Masbough, N. (2020). Products of regular locally compact spaces are k_R-spaces. <i>Topology Proceedings</i>, <i>55</i>, 35–38.","short":"H. Glöckner, N. Masbough, Topology Proceedings 55 (2020) 35–38.","chicago":"Glöckner, Helge, and Niku Masbough. “Products of Regular Locally Compact Spaces Are K_R-Spaces.” <i>Topology Proceedings</i> 55 (2020): 35–38."},"user_id":"178","volume":55,"page":"35–38","_id":"34787","language":[{"iso":"eng"}],"date_updated":"2022-12-21T20:06:44Z","article_type":"original","intvolume":"        55","status":"public","title":"Products of regular locally compact spaces are k_R-spaces","year":"2020","publication_identifier":{"issn":["0146-4124"]},"author":[{"full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge","id":"178"},{"full_name":"Masbough, Niku","first_name":"Niku","last_name":"Masbough"}]},{"abstract":[{"lang":"eng","text":"For suitable finite-dimensional smooth manifolds M (possibly with various\r\nkinds of boundary or corners), locally convex topological vector spaces F and\r\nnon-negative integers k, we construct continuous linear operators S_n from the\r\nspace of F-valued k times continuously differentiable functions on M to the\r\ncorresponding space of smooth functions such that S_n(f) converges to f in\r\nC^k(M,F) as n tends to infinity, uniformly for f in compact subsets of\r\nC^k(M,F). We also study the existence of continuous linear right inverses for\r\nrestriction maps from C^k(M,F) to C^k(L,F) if L is a closed subset of M,\r\nendowed with a C^k-manifold structure turning the inclusion map from L to M\r\ninto a C^k-map. Moreover, we construct continuous linear right inverses for\r\nrestriction operators between spaces of sections in vector bundles in many\r\nsituations, and smooth local right inverses for restriction operators between\r\nmanifolds of mappings. We also obtain smoothing results for sections in fibre\r\nbundles."}],"citation":{"ieee":"H. Glöckner, “Smoothing operators for vector-valued functions and extension operators,” <i>arXiv:2006.00254</i>. 2020.","apa":"Glöckner, H. (2020). Smoothing operators for vector-valued functions and extension operators. In <i>arXiv:2006.00254</i>.","short":"H. Glöckner, ArXiv:2006.00254 (2020).","chicago":"Glöckner, Helge. “Smoothing Operators for Vector-Valued Functions and Extension Operators.” <i>ArXiv:2006.00254</i>, 2020.","mla":"Glöckner, Helge. “Smoothing Operators for Vector-Valued Functions and Extension Operators.” <i>ArXiv:2006.00254</i>, 2020.","bibtex":"@article{Glöckner_2020, title={Smoothing operators for vector-valued functions and extension operators}, journal={arXiv:2006.00254}, author={Glöckner, Helge}, year={2020} }","ama":"Glöckner H. Smoothing operators for vector-valued functions and extension operators. <i>arXiv:200600254</i>. Published online 2020."},"publication":"arXiv:2006.00254","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"type":"preprint","date_created":"2022-12-22T07:51:53Z","external_id":{"arxiv":["2006.00254"]},"date_updated":"2022-12-22T07:52:42Z","author":[{"id":"178","full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge"}],"status":"public","year":"2020","title":"Smoothing operators for vector-valued functions and extension operators","user_id":"178","_id":"34808","language":[{"iso":"eng"}]},{"abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Given a closed orientable hyperbolic manifold of dimension <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ne 3$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>≠</mml:mo>\r\n                    <mml:mn>3</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers.\r\n</jats:p>","lang":"eng"}],"publication":"Communications in Mathematical Physics","issue":"2","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"type":"journal_article","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"date_created":"2022-05-17T12:06:06Z","intvolume":"       378","date_updated":"2022-05-19T10:13:48Z","publication_status":"published","author":[{"full_name":"Küster, Benjamin","first_name":"Benjamin","last_name":"Küster"},{"id":"49178","full_name":"Weich, Tobias","first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919"}],"publication_identifier":{"issn":["0010-3616","1432-0916"]},"title":"Pollicott-Ruelle Resonant States and Betti Numbers","year":"2020","doi":"10.1007/s00220-020-03793-2","language":[{"iso":"eng"}],"citation":{"chicago":"Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti Numbers.” <i>Communications in Mathematical Physics</i> 378, no. 2 (2020): 917–41. <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">https://doi.org/10.1007/s00220-020-03793-2</a>.","short":"B. 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Pollicott-Ruelle Resonant States and Betti Numbers. <i>Communications in Mathematical Physics</i>, <i>378</i>(2), 917–941. <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">https://doi.org/10.1007/s00220-020-03793-2</a>","bibtex":"@article{Küster_Weich_2020, title={Pollicott-Ruelle Resonant States and Betti Numbers}, volume={378}, DOI={<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Küster, Benjamin and Weich, Tobias}, year={2020}, pages={917–941} }","ama":"Küster B, Weich T. 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Auflage (Springer 2017)}, volume={67}, DOI={<a href=\"https://doi.org/10.1007/s00591-019-00254-3\">10.1007/s00591-019-00254-3</a>}, journal={Mathematische Semesterberichte}, author={Hilgert, Joachim}, year={2020}, pages={97–98} }","mla":"Hilgert, Joachim. “Daniel Grieser: Mathematisches Problemlösen und Beweisen – Eine Entdeckungsreise in die Mathematik. 2. Auflage (Springer 2017).” <i>Mathematische Semesterberichte</i>, vol. 67, 2020, pp. 97–98, doi:<a href=\"https://doi.org/10.1007/s00591-019-00254-3\">10.1007/s00591-019-00254-3</a>."},"date_created":"2024-02-20T10:06:36Z","type":"review","department":[{"_id":"91"}],"title":"Daniel Grieser: Mathematisches Problemlösen und Beweisen – Eine Entdeckungsreise in die Mathematik. 2. Auflage (Springer 2017)","year":"2020","status":"public","author":[{"full_name":"Hilgert, Joachim","first_name":"Joachim","last_name":"Hilgert","id":"220"}],"date_updated":"2024-02-20T10:10:24Z","publication_status":"published","intvolume":"        67","page":"97–98","_id":"51564","language":[{"iso":"ger"}],"doi":"10.1007/s00591-019-00254-3","user_id":"49063","volume":67},{"type":"review","department":[{"_id":"91"}],"date_created":"2024-02-20T10:05:17Z","publication":"Mathematische Semesterberichte","citation":{"chicago":"Hilgert, Joachim. “Claas Lattmann: Mathematische Modellierung bai Platon zwischen Thales und Euklid (De Gruyter 2019).” <i>Mathematische Semesterberichte</i>, 2020. <a href=\"https://doi.org/10.1007/s00591-019-00254-3\">https://doi.org/10.1007/s00591-019-00254-3</a>.","short":"J. Hilgert, Mathematische Semesterberichte 67 (2020) 109–111.","ieee":"J. Hilgert, “Claas Lattmann: Mathematische Modellierung bai Platon zwischen Thales und Euklid (De Gruyter 2019),” <i>Mathematische Semesterberichte</i>, vol. 67. pp. 109–111, 2020, doi: <a href=\"https://doi.org/10.1007/s00591-019-00254-3\">10.1007/s00591-019-00254-3</a>.","apa":"Hilgert, J. (2020). Claas Lattmann: Mathematische Modellierung bai Platon zwischen Thales und Euklid (De Gruyter 2019). In <i>Mathematische Semesterberichte</i> (Vol. 67, pp. 109–111). <a href=\"https://doi.org/10.1007/s00591-019-00254-3\">https://doi.org/10.1007/s00591-019-00254-3</a>","bibtex":"@article{Hilgert_2020, title={Claas Lattmann: Mathematische Modellierung bai Platon zwischen Thales und Euklid (De Gruyter 2019)}, volume={67}, DOI={<a href=\"https://doi.org/10.1007/s00591-019-00254-3\">10.1007/s00591-019-00254-3</a>}, journal={Mathematische Semesterberichte}, author={Hilgert, Joachim}, year={2020}, pages={109–111} }","ama":"Hilgert J. Claas Lattmann: Mathematische Modellierung bai Platon zwischen Thales und Euklid (De Gruyter 2019). <i>Mathematische Semesterberichte</i>. 2020;67:109–111. doi:<a href=\"https://doi.org/10.1007/s00591-019-00254-3\">10.1007/s00591-019-00254-3</a>","mla":"Hilgert, Joachim. “Claas Lattmann: Mathematische Modellierung bai Platon zwischen Thales und Euklid (De Gruyter 2019).” <i>Mathematische Semesterberichte</i>, vol. 67, 2020, pp. 109–111, doi:<a href=\"https://doi.org/10.1007/s00591-019-00254-3\">10.1007/s00591-019-00254-3</a>."},"doi":"10.1007/s00591-019-00254-3","user_id":"49063","volume":67,"page":"109–111","_id":"51563","language":[{"iso":"ger"}],"date_updated":"2024-02-20T10:10:28Z","publication_status":"published","intvolume":"        67","status":"public","year":"2020","title":"Claas Lattmann: Mathematische Modellierung bai Platon zwischen Thales und Euklid (De Gruyter 2019)","author":[{"first_name":"Joachim","last_name":"Hilgert","full_name":"Hilgert, Joachim"}]},{"date_updated":"2024-04-11T12:36:53Z","publication_status":"published","intvolume":"       378","year":"2020","title":"Pollicott-Ruelle Resonant States and Betti Numbers","publication_identifier":{"issn":["0010-3616","1432-0916"]},"author":[{"first_name":"Benjamin","last_name":"Küster","full_name":"Küster, Benjamin"},{"last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias","full_name":"Weich, Tobias","id":"49178"}],"doi":"10.1007/s00220-020-03793-2","language":[{"iso":"eng"}],"abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Given a closed orientable hyperbolic manifold of dimension <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ne 3$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>≠</mml:mo>\r\n                    <mml:mn>3</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers.\r\n</jats:p>","lang":"eng"}],"publication":"Communications in Mathematical Physics","issue":"2","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"type":"journal_article","department":[{"_id":"548"}],"date_created":"2024-04-11T12:33:03Z","status":"public","user_id":"70575","volume":378,"page":"917-941","publisher":"Springer Science and Business Media LLC","_id":"53415","citation":{"mla":"Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti Numbers.” <i>Communications in Mathematical Physics</i>, vol. 378, no. 2, Springer Science and Business Media LLC, 2020, pp. 917–41, doi:<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>.","bibtex":"@article{Küster_Weich_2020, title={Pollicott-Ruelle Resonant States and Betti Numbers}, volume={378}, DOI={<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Küster, Benjamin and Weich, Tobias}, year={2020}, pages={917–941} }","ama":"Küster B, Weich T. Pollicott-Ruelle Resonant States and Betti Numbers. <i>Communications in Mathematical Physics</i>. 2020;378(2):917-941. doi:<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>","ieee":"B. Küster and T. Weich, “Pollicott-Ruelle Resonant States and Betti Numbers,” <i>Communications in Mathematical Physics</i>, vol. 378, no. 2, pp. 917–941, 2020, doi: <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>.","apa":"Küster, B., &#38; Weich, T. (2020). Pollicott-Ruelle Resonant States and Betti Numbers. <i>Communications in Mathematical Physics</i>, <i>378</i>(2), 917–941. <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">https://doi.org/10.1007/s00220-020-03793-2</a>","chicago":"Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti Numbers.” <i>Communications in Mathematical Physics</i> 378, no. 2 (2020): 917–41. <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">https://doi.org/10.1007/s00220-020-03793-2</a>.","short":"B. Küster, T. Weich, Communications in Mathematical Physics 378 (2020) 917–941."}}]