@unpublished{65073, abstract = {{We study the large-time behavior of the continuous-time heat kernel and of solutions to the heat equation on homogeneous trees. First, we derive sharp asymptotic formulas for the heat kernel as $t\to\infty$. Second, using them, we show that solutions with initial data in weighted $\ell^1$ classes, asymptotically factorize in $\ell^p$ norms, $p\in[1,\infty]$, as the product of the heat kernel, times a $p$-mass function, dependent on the initial condition and $p$. The $p$-mass function is described in terms of boundary averages associated with Busemann functions for $p<2$, while for $p\ge 2$, it is expressed through convolution with the ground spherical function. For comparison, the case of the integers shows that a single constant mass determines the asymptotics of solutions to the heat equation for all $p$, emphasizing the influence of the graph geometry on heat diffusion.}}, author = {{Papageorgiou, Efthymia}}, booktitle = {{2603.11232}}, title = {{{Long-time asymptotics for the heat kernel and for heat equation solutions on homogeneous trees}}}, year = {{2026}}, } @article{53542, abstract = {{AbstractThis work deals with the extension problem for the fractional Laplacian on Riemannian symmetric spaces G/K of noncompact type and of general rank, which gives rise to a family of convolution operators, including the Poisson operator. More precisely, motivated by Euclidean results for the Poisson semigroup, we study the long-time asymptotic behavior of solutions to the extension problem for $$L^1$$ L 1 initial data. In the case of the Laplace–Beltrami operator, we show that if the initial data are bi-K-invariant, then the solution to the extension problem behaves asymptotically as the mass times the fundamental solution, but this convergence may break down in the non-bi-K-invariant case. In the second part, we investigate the long-time asymptotic behavior of the extension problem associated with the so-called distinguished Laplacian on G/K. In this case, we observe phenomena which are similar to the Euclidean setting for the Poisson semigroup, such as $$L^1$$ L 1 asymptotic convergence without the assumption of bi-K-invariance.}}, author = {{Papageorgiou, Efthymia}}, issn = {{1424-3199}}, journal = {{Journal of Evolution Equations}}, keywords = {{Mathematics (miscellaneous)}}, number = {{2}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces}}}, doi = {{10.1007/s00028-024-00959-6}}, volume = {{24}}, year = {{2024}}, } @inbook{53537, author = {{Grigor'yan, Alexander and Papageorgiou, Efthymia and Zhang, Hong-Wei}}, booktitle = {{From Classical Analysis to Analysis on Fractals. A Tribute to Robert Strichartz, Volume 1}}, editor = {{Alonso Ruiz, Patricia and Hinz, Michael and Okoudjou, Kasso A. and Rogers, Luke G. and Teplyaev, Alexander}}, isbn = {{9783031377990}}, issn = {{2296-5009}}, publisher = {{Springer International Publishing}}, title = {{{Asymptotic Behavior of the Heat Semigroup on Certain Riemannian Manifolds}}}, doi = {{10.1007/978-3-031-37800-3}}, year = {{2023}}, } @article{53540, abstract = {{AbstractThis note is concerned with two families of operators related to the fractional Laplacian, the first arising from the Caffarelli-Silvestre extension problem and the second from the fractional heat equation. They both include the Poisson semigroup. We show that on a complete, connected, and non-compact Riemannian manifold of non-negative Ricci curvature, in both cases, the solution with $$L^1$$ L 1 initial data behaves asymptotically as the mass times the fundamental solution. Similar long-time convergence results remain valid on more general manifolds satisfying the Li-Yau two-sided estimate of the heat kernel. The situation changes drastically on hyperbolic space, and more generally on rank one non-compact symmetric spaces: we show that for the Poisson semigroup, the convergence to the Poisson kernel fails -but remains true under the additional assumption of radial initial data.}}, author = {{Papageorgiou, Efthymia}}, issn = {{0926-2601}}, journal = {{Potential Analysis}}, keywords = {{Analysis}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Large-Time Behavior of Two Families of Operators Related to the Fractional Laplacian on Certain Riemannian Manifolds}}}, doi = {{10.1007/s11118-023-10109-1}}, year = {{2023}}, } @article{53539, abstract = {{AbstractThe infinite Brownian loop on a Riemannian manifold is the limit in distribution of the Brownian bridge of length T around a fixed origin when $$T \rightarrow +\infty $$ T → + ∞ . The aim of this note is to study its long-time asymptotics on Riemannian symmetric spaces G/K of noncompact type and of general rank. This amounts to the behavior of solutions to the heat equation subject to the Doob transform induced by the ground spherical function. Unlike the standard Brownian motion, we observe in this case phenomena which are similar to the Euclidean setting, namely $$L^1$$ L 1 asymptotic convergence without requiring bi-K-invariance for initial data, and strong $$L^{\infty }$$ L ∞ convergence.}}, author = {{Papageorgiou, Efthymia}}, issn = {{2296-9020}}, journal = {{Journal of Elliptic and Parabolic Equations}}, keywords = {{Applied Mathematics, Numerical Analysis, Analysis}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Asymptotics for the infinite Brownian loop on noncompact symmetric spaces}}}, doi = {{10.1007/s41808-023-00250-8}}, year = {{2023}}, } @article{53538, abstract = {{AbstractWe study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In Fotiadis and Daskaloyannis (Nonlinear Anal 214, 112546, 2022), harmonic maps are related to the sinh-Gordon equation and a Bäcklund transformation is introduced, which connects solutions of the sinh-Gordon and sine-Gordon equation. We develop this machinery in order to construct new harmonic maps to the hyperbolic plane.}}, author = {{Polychrou, G. and Papageorgiou, Efthymia and Fotiadis, A. and Daskaloyannis, C.}}, issn = {{1139-1138}}, journal = {{Revista Matemática Complutense}}, keywords = {{General Mathematics}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation}}}, doi = {{10.1007/s13163-023-00476-z}}, year = {{2023}}, }