Giovanni Catino
Published 2014-10-09Version 1
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.
Compact stable surfaces with constant mean curvature in Killing submersions
A half-space theorem for graphs of constant mean curvature $0<H<\frac{1}{2}$ in $\mathbb{H}^2\times\mathbb{R}$
Conformal Deformation to Scalar Flat Metrics with Constant Mean Curvature on the Boundary in Higher Dimensions
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