English

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 Rn,1\mathbb R^{n,1}. 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