English

Sobolev Inequalities In Manifolds With Asymptotically Nonnegative Curvature

Differential Geometry 2022-06-17 v2

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.

Keywords

Cite

@article{arxiv.2203.14624,
  title  = {Sobolev Inequalities In Manifolds With Asymptotically Nonnegative Curvature},
  author = {Yuxin Dong and Hezi Lin and Lingen Lu},
  journal= {arXiv preprint arXiv:2203.14624},
  year   = {2022}
}

Comments

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