Related papers: Remark About Heat Diffusion on Periodic Spaces

We analyze the heat kernel associated to the Laplacian on a compact metric graph, with standard Kirchoff-Neumann vertex conditions. An explicit formula for the heat kernel as a sum over loops, developed by Roth and Kostrykin, Potthoff, and…

We discuss the heat content asymptotics associated with the heat flow out of a smooth compact manifold in a larger compact Riemannian manifold. Although there are no boundary conditions, the corresponding heat content asymptotics involve…

Let $(M, g)$ be a smooth n-dimensional Riemannian manifold for $n\ge 2$. Consider the conformal perturbation $\tilde{g}=h g$ where $h$ is a smooth bounded positive function on $M$. Denote by $\tilde{p}_t(x,y)$ the heat kernel of manifolds…

This paper is twofold. The first part aims to study the long-time asymptotic behavior of solutions to the heat equation on Riemannian symmetric spaces $G/K$ of noncompact type and of general rank. We show that any solution to the heat…

We show that, on a complete, connected and non-compact Riemannian manifold of non-negative Ricci curvature, the solution to the heat equation with $L^{1}$ initial data behaves asymptotically as the mass times the heat kernel. In contrast to…

We prove that a metric measure space equipped with a Dirichlet form admitting an Euclidean heat kernel is necessarily isometric to the Euclidean space. This helps us providing an alternative proof of Colding's celebrated almost rigidity…

For Riemannian symmetric spaces $X=G/K$ of noncompact type, we show that for all left $K$-invariant $f\in L^1(X)$, the functions $\|h_t\|_{L^p(X)}^{-1}(f\ast h_t-M_p(f)h_t)$ (with $h_t$ being the heat kernel of $X$) converges to zero in…

In this paper, we study sharp two-sided heat kernel estimates for a large class of symmetric reflected diffusions with jumps on the closure of an inner uniform domain $D$ in a length metric space. The length metric is the intrinsic metric…

Let $\Omega$ be an open set in a complete, smooth, non-compact, $m$-dimensional Riemannian manifold $M$ without boundary, where $M$ satisfies a two-sided Li-Yau gaussian heat kernel bound. It is shown that if $\Omega$ has infinite measure,…

Assuming the heat kernel on a doubling Dirichlet metric measure space has a sub-Gaussian bound, we prove an asymptotically sharp spectral upper bound on the survival probability of the associated diffusion process. As a consequence, we can…

Let $M$ be a complete Riemannian manifold and $D\subset M$ a smoothly bounded domain with compact closure. We use Brownian motion and the classic results on the Stieltjes moment problem to study the relationship between the Dirichlet…

Given an RCD$(K,N)$ space $({X},\mathsf{d},\mathfrak{m})$, one can use its heat kernel $\rho$ to map it into the $L^2$ space by a locally Lipschitz map $\Phi_t(x):=\rho(x,\cdot,t)$. The space $(X,\mathsf{d},\mathfrak{m})$ is said to be an…

We give sharp asymptotic estimates at infinity of all radial partial derivatives of the heat kernel on H-type groups. As an application, we give a new proof of the discreteness of the spectrum of some natural sub-Riemannian…

We study the relationship between the geometry and the Laplace spectrum of a Riemannian orbifold O via its heat kernel; as in the manifold case, the time-zero asymptotic expansion of the heat kernel furnishes geometric information about O.…

The covariant technique for calculating the heat kernel asymptotic expansion for an elliptic differential second order operator is generalized to manifolds with boundary. The first boundary coefficients of the asymptotic expansion which are…

We establish an estimate for the fundamental solution of the heat equation on a closed Riemannian manifold $M$ of dimension at least 3, evolving under the Ricci flow. The estimate depends on some constants arising from a Sobolev imbedding…

We study the behavior of the heat kernel of the Hodge Laplacian on a contact manifold endowed with a family of Riemannian metrics that blow-up the directions transverse to the contact distribution. We apply this to analyze the behavior of…

The heat kernel expansion for a general non--minimal operator on the spaces $C^\infty (\Lambda^k)$ and $C^\infty (\Lambda^{p,q})$ is studied. The coefficients of the heat kernel asymptotics for this operator are expressed in terms of the…

The high temperature asymptotics of the Helmholtz free energy of electromagnetic field subjected to boundary conditions with spherical and cylindrical symmetries are constructed by making use of a general expansion in terms of heat kernel…

We study the small-time asymptotics of the heat content of smooth non-characteristic domains of a general rank-varying sub-Riemannian structure, equipped with an arbitrary smooth measure. By adapting to the sub-Riemannian case a technique…