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arXiv · 1707.03323

Nonnegatively curved hypersurfaces with free boundary on a sphere

Mohammad Ghomi·Changwei Xiong
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Abstract

We prove that in Euclidean space $R^{n+1}$ any compact immersed nonnegatively curved hypersurface $M$ with free boundary on the sphere $S^n$ is an embedded convex topological disk. In particular, when the $m^{th}$ mean curvature of $M$ is constant, for any $1\leq m\leq n$, $M$ is a spherical cap or an equatorial disk.

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Mohammad Ghomi, Changwei Xiong. 2017-07-11. Nonnegatively curved hypersurfaces with free boundary on a sphere. https://arxiv.org/abs/1707.03323

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