Sobolev Inequalities In Manifolds With Asymptotically Nonnegative Curvature

Abstract

Using the ABP-method as in a recent work by Brendle, we establish some sharp Sobolev and isoperimetric inequalities for compact domains and submanifolds in a complete Riemannian manifold with asymptotically nonnegative curvature. These inequalities generalize those given by Brendle in the case of complete Riemannian manifolds with nonnegative curvature.

In this version, we correct some typos and update the references