Abstract
We consider the integrals of the $r$-mean curvatures $S_r$ of a complete hypersurface $M$ in the space form $\mathcal{Q}_c^{n+1}$. Among other results, we prove that $\int_MS_r\,dM=\infty$ for a complete properly immersed hypersurfaces in a space form with $S_r\geq0$, $S_r\not\equiv0$ and $S_{r+1}\equiv0$ for some $r\le n-1$.
Citation
Hilário Alencar. Walcy Santos. Detang Zhou. "Curvature integral estimates for complete hypersurfaces." Illinois J. Math. 55 (1) 185 - 203, Spring 2011. https://doi.org/10.1215/ijm/1355927033
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