Related papers: The Robin heat kernel and its expansion via Robin …

In this note we establish the large time non-negativity of the heat kernel for a class of elliptic differential operators on closed, Riemannian manifolds, and apply this result to a problem from conformal differential geometry.

This paper is devoted to investigate the heat trace asymptotic expansion corresponding to the magnetic Steklov eigenvalue problem on Riemannian manifolds with boundary. We establish an effective procedure, by which we can calculate all the…

The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients…

The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented…

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…

In the sub-Riemannian manifolds, on the one hand, following Baudoin-Garofalo \cite{BaudoinGarofalo}, the upper bound for heat kernels associated to a class of locally subelliptic operators are given under the generalized curvature-dimension…

In this paper we give Hamilton's Laplacian estimates for the heat equation on complete noncompact manifolds with nonnegative Ricci curvature. As an application, combining Li-Yau's lower and upper bounds of the heat kernel, we give an…

D.Freed has formulated and proved an index theorem on odd dimensional spin manifolds with boundary. The proof is based on analysis by Calderon and Seeley. In this note we are going to give a proof of this theorem using the heat kernels…

We prove heat kernel estimates for the $\bar\partial$-Neumann Laplacian acting in spaces of differential forms over noncompact, strongly pseudoconvex complex manifolds with a Lie group symmetry and compact quotient. We also relate our…

We use heat kernels or eigenfunctions of the Laplacian to construct local coordinates on large classes of Euclidean domains and Riemannian manifolds (not necessarily smooth, e.g. with $\mathcal{C}^\alpha$ metric). These coordinates are…

The third eigenvalue of the Robin Laplacian on a simply-connected planar domain of given area is bounded above by the corresponding eigenvalue of a disjoint union of two equal disks, for Robin parameters in $[-4\pi,4\pi]$. This sharp…

We consider the first Robin eigenvalue $\l_p(M,\a)$ for the $p$-Laplacian on a compact Riemannian manifold $M$ with nonempty smooth boundary, with $\a \in \R$ being the Robin parameter. Firstly, we prove eigenvalue comparison theorems of…

In this note we consider achieving the largest principle eigenvalue of a Robin Laplacian on a bounded domain $\Omega$ by optimizing the Robin parameter function under an integral constraint. The main novelty of our approach lies in…

We demonstrate lower bounds for the eigenvalues of compact Bakry-Emery manifolds with and without boundary. The lower bounds for the first eigenvalue rely on a generalised maximum principle which allows gradient estimates in the Riemannian…

The relative heat content associated with a subset $\Omega\subset M$ of a sub-Riemannian manifold, is defined as the total amount of heat contained in $\Omega$ at time $t$, with uniform initial condition on $\Omega$, allowing the heat to…

This paper investigates the asymptotic behavior of a class of nonlinear variational problems with Robin-type boundary conditions on a bounded Lipschitz domain. The energy functional contains a bulk term (the $p$-norm of the gradient), a…

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,…

Aim of this short note is to show that a dimension-free Harnack inequality on an infinitesimally Hilbertian metric measure space where the heat semigroup admits an integral representation in terms of a kernel is suffcient to deduce a sharp…

In this paper we extend a gradient estimate of R. Hamilton for positive solutions to the heat equation on closed manifolds to bounded positive solutions on complete, non-compact manifolds with $Rc \geq -Kg$. We accomplish this extension via…

Let $M$ be a complete connected Riemannian manifold with boundary $\pp M$, $Q$ a bounded continuous function on $\pp M$, and $L= \DD+Z$ for a $C^1$-vector field $Z$ on $M$. By using the reflecting diffusion process generated by $L$ and its…