Sobolev inequalities in manifolds with asymptotically nonnegative curvature
摘要
Using the ABP-method as in a recent work by Brendle (Commun Pure Appl Math 76:2192–2218, 2022), we establish some sharp Sobolev and isoperimetric inequalities for compact domains and submanifolds in a complete Riemannian manifold with asymptotically nonnegative Ricci/sectional curvature. These inequalities generalize those given by Brendle in the case of complete Riemannian manifolds with nonnegative curvature.