Harnack inequalities on manifolds with boundary and applications

Abstract: 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 the Neumann heat kernel w.r.t. a volume type measure μ and for K a constant, the curvature condition 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. [ABSTRACT FROM AUTHOR]