Sharp estimates and inequalities on Riemannian manifolds with Euclidean volume growth

Abstract

We obtain sharp estimates for heat kernels and Green's functions on complete noncompact Riemannian manifolds with Euclidean volume growth and nonnegative Ricci curvature. We will then apply these estimates to obtain sharp Moser-Trudinger inequalities on such manifolds.

38 pages. In v.2 sharpness statements were added in Theorem 1 and Theorem 2. Section 6, containing the proofs of such statements, was revised accordingly. Several comments were added after the statement of Theorem 2. Few minor revisions and corrections