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.
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