Illinois Journal of Mathematics

Curvature integral estimates for complete hypersurfaces

Hilário Alencar, Walcy Santos, and Detang Zhou

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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 $r\le n-1$.

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Illinois J. Math., Volume 55, Number 1 (2011), 185-203.

First available in Project Euclid: 19 December 2012

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Zentralblatt MATH identifier

Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]


Alencar, Hilário; Santos, Walcy; Zhou, Detang. Curvature integral estimates for complete hypersurfaces. Illinois J. Math. 55 (2011), no. 1, 185--203. doi:10.1215/ijm/1355927033.

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