English

Sobolev inequalities in manifolds with nonnegative curvature

Differential Geometry 2022-05-31 v5

Abstract

We prove a sharp Sobolev inequality on manifolds with nonnegative Ricci curvature. Moreover, we prove a Michael-Simon inequality for submanifolds in manifolds with nonnegative sectional curvature. Both inequalities depend on the asymptotic volume ratio of the ambient manifold.

Keywords

Cite

@article{arxiv.2009.13717,
  title  = {Sobolev inequalities in manifolds with nonnegative curvature},
  author = {S. Brendle},
  journal= {arXiv preprint arXiv:2009.13717},
  year   = {2022}
}

Comments

final version, to appear in Comm Pure Appl Math