✦ LIBER ✦

Harnack inequalities on manifolds with boundary and applications

✍ Scribed by Feng-Yu Wang

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 215 KB
Volume: 94
Category: Article
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2010.03.001

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✦ Synopsis

On a large class of Riemannian 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 particular, for p t (x, y) the Neumann heat kernel w.r.t. a volume type measure μ and for K a constant, the curvature condition Ric -∇Z K together with the convexity of the boundary is equivalent to the heat kernel entropy inequality:

where ρ is the Riemannian distance. The main result is partly extended to manifolds with non-convex boundary and applied to derive the HWI inequality.

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