Pure Maths Colloquium: Dimension-free Harnack inequalities and applications
12 May 2014 16:00 in CM221
Explicit Dimension-free Harnack inequalities of (Neumann) heat semigroups on Riemannian manifolds (possibly with boundary) are introduced. These inequalities are equivalent to the curvature lower bound condition as well as the convexity of the boundary, and have a number of applications to functional inequalities, heat kernel estimates and transportation cost inequalities. Extensions to manifolds with non-convex boundary are also discussed.
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