Sobolev Inequalities in Spacelike Submanifolds of Minkowski Space
Differential Geometry
2023-04-10 v1
Abstract
We follow the method of ABP estimate in \cite{brendle2021} and apply it to spacelike submanifolds in . We then obtain Michael-Simon type inequalities. Surprisingly, our investigation leads to a Sobolev inequality without a mean curvature term, provided the hypersurface is mean convex.
Keywords
Cite
@article{arxiv.2304.03478,
title = {Sobolev Inequalities in Spacelike Submanifolds of Minkowski Space},
author = {Liang Xu},
journal= {arXiv preprint arXiv:2304.03478},
year = {2023}
}
Comments
15 pages; 3 figures