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

created by catino on 09 Oct 2014
modified on 08 Oct 2016

[BibTeX]

Published Paper

Inserted: 9 oct 2014
Last Updated: 8 oct 2016

Journal: Bull. Sci. Math.
Volume: 140
Number: 8
Pages: 901-907
Year: 2016

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 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.