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

Abstract

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}.