A remark on compact hypersurfaces with constant mean curvature in space forms

Giovanni Catino

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arXiv · 1410.2404

A remark on compact hypersurfaces with constant mean curvature in space forms

Giovanni Catino

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Abstract

In this note we characterize compact hypersurfaces of dimension $n\geq 2$ with constant mean curvature $H$ immersed in space forms of constant curvature and satisfying an optimal integral pinching condition: they are either totally umbilical or, when $n\geq 3$ and $H\neq 0$, they are locally contained in a rotational hypersurface. In dimension two, the integral pinching condition reduces to a topological assumption and we recover the classical Hopf-Chern result.

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Giovanni Catino. 2014-10-09. A remark on compact hypersurfaces with constant mean curvature in space forms. https://arxiv.org/abs/1410.2404

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