Illinois Journal of Mathematics

Curvature integral estimates for complete hypersurfaces

Hilário Alencar, Walcy Santos, and Detang Zhou

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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 $r\le n-1$.

Article information

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

Dates
First available in Project Euclid: 19 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1355927033

Digital Object Identifier
doi:10.1215/ijm/1355927033

Mathematical Reviews number (MathSciNet)
MR3006685

Zentralblatt MATH identifier
1260.53110

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

Citation

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. https://projecteuclid.org/euclid.ijm/1355927033


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