Convexity of $\lambda$-hypersurfaces

Tang-Kai Lee

Convexity of $\lambda$-hypersurfaces

Differential Geometry 2021-06-21 v2 Analysis of PDEs

Authors: Tang-Kai Lee

Abstract

We prove that any $n$ -dimensional closed mean convex $\lambda$ -hypersurface is convex if $\lambda\le 0.$ This generalizes Guang's work on $2$ -dimensional strictly mean convex $\lambda$ -hypersurfaces. As a corollary, we obtain a gap theorem for closed $\lambda$ -hypersurfaces with $\lambda\le 0.$

Keywords

hypersurfaces convex geometry convex bodies

Cite

@article{arxiv.2104.05464,
  title  = {Convexity of $\lambda$-hypersurfaces},
  author = {Tang-Kai Lee},
  journal= {arXiv preprint arXiv:2104.05464},
  year   = {2021}
}

Comments

10 pages; minor changes suggested by the referee

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