An estimate for the scalar curvature of constant mean curvature hypersurfaces in space forms (Q658538)

Let \(\Sigma^n\) be a hypersurface of constant mean curvature and with two principal curvatures, which is immersed into an \((n+1)\)-dimensional space form \(\mathbb M_c^{n+1}\), \(c=0,-1,1\), \(n\geqslant2\). In a series of theorems, the authors derive sharp estimates for the supremum of the scalar curvature (equivalently, the infimum of the squared norm ofthe second fundamental form) of \(\Sigma^n\). The obtained results generalize many already known properties of such hypersurfaces. In the proofs, the generalized Omori-Yau principle is applied.