Harnack inequalities on manifolds with boundary and applications
type: Item
instance of: scholarly article
title: Harnack inequalities on manifolds with boundary and applications
zbMATH Open document ID: 1207.58028
author: Feng-Yu Wang
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2010-10-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/0908.2888
review text: It is known that on a large class of manifolds with boundary, some dimension-free Harnack inequalities for the Neumann semigroup are proved to be equivalent to the convexity of the boundary and a curvature condition. In this paper this result is partly extended to manifolds with non-convex boundary and applied to derive the HWI inequality.
Mathematics Subject Classification ID: 58J60
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 5798153
zbMATH Keywords: curvature
zbMATH Keywords: Harnack inequality
zbMATH Keywords: heat kernel
zbMATH Keywords: second fundamental form
reviewed by: Yuri E. Gliklikh
MaRDI profile type: Publication
OpenAlex ID: W2081910629
arXiv ID: 0908.2888
Wikidata QID: Q125294135
cites work: Q3676923
cites work: Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator
cites work: Hypercontractivity of Hamilton-Jacobi equations.
cites work: Lower bounds for the eigenvalues of Riemannian manifolds
cites work: Multiplicative functional for the heat equation on manifolds with boundary.
cites work: Q3700423
cites work: On Laplacian and Hessian comparison theorems
cites work: The geometry of Markov diffusion generators
cites work: Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
cites work: Transport inequalities, gradient estimates, entropy and Ricci curvature
cites work: Application of coupling methods to the Neumann eigenvalue problem
cites work: Logarithmic Sobolev inequalities on noncompact Riemannian manifolds
cites work: Equivalence of dimension-free Harnack inequality and curvature condition
cites work: Gradient estimates and the first Neumann eigenvalue on manifolds with boundary
cites work: Estimates of the first Neumann eigenvalue and the log‐Sobolev constant on non‐convex manifolds
cites work: Second fundamental form and gradient of Neumann semigroups
cites work: Semigroup properties for the second fundamental form
DOI: 10.1016/J.MATPUR.2010.03.001
description: scientific article