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