Dimension-Free Harnack Inequality and its Applications

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  • School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;

Published date: 05 Mar 2006

Abstract

This paper presents a self-contained account concerning a dimensionfree Harnack inequality and its applications. This new type of inequality not only implies heat kernel bounds as the classical Li Yau s Harnack inequality did, but also provides a direct way to describe various dimension-free properties of finite and infinite-dimensional diffusion semigroups. The author starts with a standard weighted Laplace operator on a Riemannian manifold with curvature bounded from below, and then move further to the unbounded below curvature case and its infinite-dimensional settings.

Cite this article

WANG Feng-Yu . Dimension-Free Harnack Inequality and its Applications[J]. Frontiers of Mathematics in China, 2006 , 1(1) : 53 -72 . DOI: 10.1007/s11464-005-0021-3

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