{"abstract":[{"text":"We study the influence of the intrinsic curvature on the large time behaviour of the heat equation in a tubular neighbourhood of an unbounded geodesic in a two-dimensional Riemannian manifold. Since we consider killing boundary conditions, there is always an exponential-type decay for the heat semigroup. We show that this exponential-type decay is slower for positively curved manifolds comparing to the flat case. As the main result, we establish a sharp extra polynomial-type decay for the heat semigroup on negatively curved manifolds comparing to the flat case. The proof employs the existence of Hardy-type inequalities for the Dirichlet Laplacian in the tubular neighbourhoods on negatively curved manifolds and the method of self-similar variables and weighted Sobolev spaces for the heat equation.","lang":"eng"}],"date_created":"2022-09-14T05:18:39Z","volume":4,"doi":"https://doi.org/10.4171/jst/69","issue":"2","publication_status":"published","publication":"Journal of Spectral Theory","citation":{"ieee":"M. Kolb and D. Krejčiřík, “The Brownian traveller on manifolds,” <i>Journal of Spectral Theory</i>, vol. 4, no. 2, pp. 235–281, 2014, doi: <a href=\"https://doi.org/10.4171/jst/69\">https://doi.org/10.4171/jst/69</a>.","mla":"Kolb, Martin, and David Krejčiřík. “The Brownian Traveller on Manifolds.” <i>Journal of Spectral Theory</i>, vol. 4, no. 2, EMS Press, 2014, pp. 235–81, doi:<a href=\"https://doi.org/10.4171/jst/69\">https://doi.org/10.4171/jst/69</a>.","short":"M. Kolb, D. Krejčiřík, Journal of Spectral Theory 4 (2014) 235–281.","ama":"Kolb M, Krejčiřík D. The Brownian traveller on manifolds. <i>Journal of Spectral Theory</i>. 2014;4(2):235-281. doi:<a href=\"https://doi.org/10.4171/jst/69\">https://doi.org/10.4171/jst/69</a>","chicago":"Kolb, Martin, and David Krejčiřík. “The Brownian Traveller on Manifolds.” <i>Journal of Spectral Theory</i> 4, no. 2 (2014): 235–81. <a href=\"https://doi.org/10.4171/jst/69\">https://doi.org/10.4171/jst/69</a>.","apa":"Kolb, M., &#38; Krejčiřík, D. (2014). The Brownian traveller on manifolds. <i>Journal of Spectral Theory</i>, <i>4</i>(2), 235–281. <a href=\"https://doi.org/10.4171/jst/69\">https://doi.org/10.4171/jst/69</a>","bibtex":"@article{Kolb_Krejčiřík_2014, title={The Brownian traveller on manifolds}, volume={4}, DOI={<a href=\"https://doi.org/10.4171/jst/69\">https://doi.org/10.4171/jst/69</a>}, number={2}, journal={Journal of Spectral Theory}, publisher={EMS Press}, author={Kolb, Martin and Krejčiřík, David}, year={2014}, pages={235–281} }"},"department":[{"_id":"96"}],"_id":"33362","author":[{"id":"48880","full_name":"Kolb, Martin","first_name":"Martin","last_name":"Kolb"},{"full_name":"Krejčiřík, David","first_name":"David","last_name":"Krejčiřík"}],"title":"The Brownian traveller on manifolds","intvolume":"         4","status":"public","user_id":"85821","language":[{"iso":"eng"}],"year":"2014","date_updated":"2022-09-14T05:18:42Z","type":"journal_article","page":"235-281","publisher":"EMS Press"}