On the scalar curvature of constant mean curvature hypersurfaces in space forms

Details On the scalar curvature of constant mean curvature hypersurfaces in space forms On the scalar curvature of constant mean curvature hypersurfaces in space forms

2009-02-25

arxiv.org/abs/0902.4486v4

Mathematics

Differential Geometry

Final version (August 2009). To appear in Journal of Mathematical Analysis and Applications. Dedicated to Professor Marcos Daj

Scientific paper

In this paper we study the behavior of the scalar curvature $S$ of a complete
hypersurface immersed with constant mean curvature into a Riemannian space form
of constant curvature, deriving a sharp estimate for the infimum of $S$. Our
results will be an application of a weak Omori-Yau maximum principle due to
Pigola, Rigoli and Setti \cite{PRS}.

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