@unpublished{65073,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}},
}

@unpublished{65546,
  abstract     = {{In this paper we study a variant of the uncentred Hardy--Littlewood maximal operator on Damek--Ricci spaces in which balls are replaced by suitable half balls. Perhaps surprisingly, such modified maximal operator has better boundedness properties than the classical one. In particular, it satisfies an $L\log L$ endpoint estimate and it is bounded on $L^p$ for every $p$ in $(1,\infty]$.}},
  author       = {{Chalmoukis, Nikolaos and Meda, Stefano and Papageorgiou, Efthymia and Santagati, Federico}},
  booktitle    = {{arXiv:2604.27839}},
  title        = {{{Uncentred maximal operators with respect to half balls on Damek--Ricci spaces}}},
  year         = {{2026}},
}

@article{64266,
  author       = {{Papageorgiou, Efthymia and Trojan, Bartosz}},
  journal      = {{Mathematische Annalen}},
  number       = {{30}},
  title        = {{{Mass Functions and Asymptotic Behavior of Caloric Functions on Affine Buildings}}},
  volume       = {{395}},
  year         = {{2026}},
}

@article{63505,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>The main goal of this work is to study the $L^{p}$-asymptotic behavior of solutions to the heat equation on arbitrary rank Riemannian symmetric spaces of non-compact-type $G/K$ for non-bi-$K$ invariant initial data. For initial data $u_{0}$ compactly supported or in a weighted $L^{1}(G/K)$ space with a weight depending on $p\in [1, \infty ]$, we introduce a mass function $M_{p}(u_{0})(\cdot )$, and prove that if $h_{t}$ is the heat kernel on $G/K$, then $$ \begin{align*} &amp;\|h_t\|_p^{-1}\,\|u_0\ast h_t \, - \,M_p(u_0)(\cdot)\,h_t\|_p \rightarrow 0 \quad \textrm{as} \quad t\rightarrow \infty.\end{align*} $$ Interestingly, the $L^{p}$ heat concentration leads to completely different expressions of the mass function for $1\leq p &amp;lt;2$ and $2\leq p\leq \infty $. If we further assume that the initial data are bi-$K$-invariant, then our mass function boils down to the constant $\int _{G/K}u_{0}$ in the case $p=1$, and more generally to $\mathcal{H}{u_{0}}(i\rho (2/p-1))$ if $1\leq p&amp;lt;2$, and to $\mathcal{H}{u_{0}}(0)$ if $2\leq p \leq \infty $. Thus, we improve upon results by Vázquez, Anker et al., and Naik et al., clarifying the nature of the problem.</jats:p>}},
  author       = {{Papageorgiou, Efthymia}},
  issn         = {{1073-7928}},
  journal      = {{International Mathematics Research Notices}},
  number       = {{7}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{<i>L</i>          p Asymptotics for the Heat Equation on Symmetric Spaces for Non-symmetric Solutions}}},
  doi          = {{10.1093/imrn/rnaf074}},
  volume       = {{2025}},
  year         = {{2025}},
}

@unpublished{64267,
  abstract     = {{Let $\mathbb{H}^n$ be the $n$-dimensional real hyperbolic space, $Δ$ its nonnegative Laplace--Beltrami operator whose bottom of the spectrum we denote by $λ_{0}$, and $σ\in (0,1)$.
  The aim of this paper is twofold. On the one hand, we determine the Fujita exponent for the fractional heat equation \[\partial_{t} u + Δ^σu = e^{βt}|u|^{γ-1}u,\] by proving that nontrivial positive global solutions exist if and only if $γ\geq 1 + β/ λ_{0}^σ$. On the other hand, we prove the existence of non-negative, bounded and finite energy solutions of the semilinear fractional elliptic equation \[
  Δ^σ v - λ^σ v - v^γ=0 \] for $0\leq λ\leq λ_{0}$ and $1<γ< \frac{n+2σ}{n-2σ}$. The two problems are known to be connected and the latter, aside from its independent interest, is actually instrumental to the former.
  \smallskip
  At the core of our results stands a novel fractional Poincaré-type inequality expressed in terms of a new scale of $L^{2}$ fractional Sobolev spaces, which sharpens those known so far, and which holds more generally on Riemannian symmetric spaces of non-compact type. We also establish an associated Rellich--Kondrachov-like compact embedding theorem for radial functions, along with other related properties.}},
  author       = {{Bruno, Tommaso and Papageorgiou, Efthymia}},
  booktitle    = {{arXiv:2509.12349}},
  title        = {{{Blow-up exponents and a semilinear elliptic equation for the fractional Laplacian on hyperbolic spaces}}},
  year         = {{2025}},
}

@article{63500,
  abstract     = {{<jats:title>Abstract</jats:title>
          <jats:p>We prove various estimates for the asymptotics of counting functions associated to point sets of coherent frames and Riesz sequences. The obtained results recover the necessary density conditions for coherent frames and Riesz sequences for general unimodular amenable groups, while providing more precise estimates under additional localization conditions on the coherent system for groups of polynomial growth. 
</jats:p>}},
  author       = {{Papageorgiou, Efthymia and van Velthoven, Jordy Timo}},
  issn         = {{0373-3114}},
  journal      = {{Annali di Matematica Pura ed Applicata (1923 -)}},
  number       = {{4}},
  pages        = {{1469--1491}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Counting function estimates for coherent frames and Riesz sequences}}},
  doi          = {{10.1007/s10231-024-01535-y}},
  volume       = {{204}},
  year         = {{2024}},
}

@article{53542,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>This work deals with the extension problem for the fractional Laplacian on Riemannian symmetric spaces <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic> 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 <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:msup>
                    <mml:mi>L</mml:mi>
                    <mml:mn>1</mml:mn>
                  </mml:msup>
                </mml:math></jats:alternatives></jats:inline-formula> initial data. In the case of the Laplace–Beltrami operator, we show that if the initial data are bi-<jats:italic>K</jats:italic>-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-<jats:italic>K</jats:italic>-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 <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic>. In this case, we observe phenomena which are similar to the Euclidean setting for the Poisson semigroup, such as <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:msup>
                    <mml:mi>L</mml:mi>
                    <mml:mn>1</mml:mn>
                  </mml:msup>
                </mml:math></jats:alternatives></jats:inline-formula> asymptotic convergence without the assumption of bi-<jats:italic>K</jats:italic>-invariance.</jats:p>}},
  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}},
}

@article{63502,
  abstract     = {{<jats:title>Abstract</jats:title>
          <jats:p>Let <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\mu $$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mi>μ</mml:mi>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> be a radial compactly supported distribution on a harmonic <jats:italic>NA</jats:italic> group. We prove that the right convolution operator <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$c_{\mu }:f \mapsto f* \mu $$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:msub>
                      <mml:mi>c</mml:mi>
                      <mml:mi>μ</mml:mi>
                    </mml:msub>
                    <mml:mo>:</mml:mo>
                    <mml:mi>f</mml:mi>
                    <mml:mo>↦</mml:mo>
                    <mml:mi>f</mml:mi>
                    <mml:mrow/>
                    <mml:mo>∗</mml:mo>
                    <mml:mi>μ</mml:mi>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> maps the space of smooth <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\mathfrak {v}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mi>v</mml:mi>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>-radial functions onto itself if and only if the spherical Fourier transform <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\widetilde{\mu }(\lambda )$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mover>
                      <mml:mi>μ</mml:mi>
                      <mml:mo>~</mml:mo>
                    </mml:mover>
                    <mml:mrow>
                      <mml:mo>(</mml:mo>
                      <mml:mi>λ</mml:mi>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>, <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\lambda \in \mathbb {C}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>λ</mml:mi>
                    <mml:mo>∈</mml:mo>
                    <mml:mi>C</mml:mi>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>, is slowly decreasing. As an application, we prove that certain averages over spheres are surjective on the space of smooth <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\mathfrak {v}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mi>v</mml:mi>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>-radial functions.</jats:p>}},
  author       = {{Papageorgiou, Efthymia}},
  issn         = {{1050-6926}},
  journal      = {{The Journal of Geometric Analysis}},
  number       = {{1}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Surjectivity of Convolution Operators on Harmonic NA Groups}}},
  doi          = {{10.1007/s12220-024-01837-w}},
  volume       = {{35}},
  year         = {{2024}},
}

@article{63504,
  author       = {{Kolountzakis, Mihail N. and Papageorgiou, Efthymia}},
  issn         = {{1948-206X}},
  journal      = {{Analysis &amp; PDE}},
  number       = {{1}},
  pages        = {{93--108}},
  publisher    = {{Mathematical Sciences Publishers}},
  title        = {{{Large sets containing no copies of a given infinite sequence}}},
  doi          = {{10.2140/apde.2025.18.93}},
  volume       = {{18}},
  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{53538,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>We 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.</jats:p>}},
  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}},
}

@article{53540,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>This 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 <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                <mml:msup>
                  <mml:mi>L</mml:mi>
                  <mml:mn>1</mml:mn>
                </mml:msup>
              </mml:math></jats:alternatives></jats:inline-formula> 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.</jats:p>}},
  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     = {{<jats:title>Abstract</jats:title><jats:p>The infinite Brownian loop on a Riemannian manifold is the limit in distribution of the Brownian bridge of length <jats:italic>T</jats:italic> around a fixed origin when <jats:inline-formula><jats:alternatives><jats:tex-math>$$T \rightarrow +\infty $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                <mml:mrow>
                  <mml:mi>T</mml:mi>
                  <mml:mo>→</mml:mo>
                  <mml:mo>+</mml:mo>
                  <mml:mi>∞</mml:mi>
                </mml:mrow>
              </mml:math></jats:alternatives></jats:inline-formula>. The aim of this note is to study its long-time asymptotics on Riemannian symmetric spaces <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic> 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 <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                <mml:msup>
                  <mml:mi>L</mml:mi>
                  <mml:mn>1</mml:mn>
                </mml:msup>
              </mml:math></jats:alternatives></jats:inline-formula> asymptotic convergence without requiring bi-<jats:italic>K</jats:italic>-invariance for initial data, and strong <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^{\infty }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                <mml:msup>
                  <mml:mi>L</mml:mi>
                  <mml:mi>∞</mml:mi>
                </mml:msup>
              </mml:math></jats:alternatives></jats:inline-formula> convergence.</jats:p>}},
  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}},
}