Heat kernel on a manifold with a local Harnack inequality
type: Item
instance of: scholarly article
title: Heat kernel on a manifold with a local Harnack inequality
zbMATH Open document ID: 0845.58056
author: A. A. Grigor'yan
published in: Communications in Analysis and Geometry
publication date: 1996-09-16T00:00:00Z
review text: The author introduces a broad class of the so-called locally Harnack manifolds, which includes in particular the manifolds with \(C^k\)-bounded geometries, with (simply) bounded geometries and with weak bounded geometries. For those manifolds (i.e. not only for bounded geometries as previously) under a certain additional condition the author gives a direct proof of the fact that the heat kernel decays at least as fast as \(1/t^{1/2}\). Another sort of results for those manifolds deals with (classical and modified) isoperimetric properties. In particular a lower bound for the first Dirichlet eigenvalue is established, etc.
reviewed by: Yuri E. Gliklikh
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 58J60
Mathematics Subject Classification ID: 58J35
zbMATH DE Number: 820211
zbMATH Keywords: Riemannian manifolds
zbMATH Keywords: heat kernels
zbMATH Keywords: Harnack inequality
zbMATH Keywords: isoperimetric inequality
MaRDI profile type: Publication
full work available at URL: cag.1994.v2.n1.a7
OpenAlex ID: W2620901024
DOI: 10.4310/CAG.1994.V2.N1.A7
description: scientific article; zbMATH DE number 820211