Curvature integral estimates for complete hypersurfaces

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dc.creatorAlencar, Hilário
dc.creatorSantos, Walcy
dc.creatorZhou, Detang
dc.date2009-03-11
dc.date.accessioned2026-07-07T12:51:39Z
dc.date.available2026-07-07T12:51:39Z
dc.descriptionWe consider the integrals of $r$-mean curvatures $S_r$ of a complete hypersurface $M$ in space forms $\mathcal{Q}_c^{n+1}$ which generalize volume $(r=0)$, total mean curvature $(r=1)$, total scalar curvature $(r=2)$ and total curvature $(r=n)$. Among other results we prove that a complete properly immersed hypersurface of a space form with $S_r\geq 0$, $S_r\not\equiv 0$ and $S_{r+1}\equiv 0$ for some $r\le n-1$ has $\int_MS_rdM=\infty.$
dc.identifierhttps://arxiv.org/abs/0903.2035
dc.identifierhttp://arxiv.org/abs/0903.2035
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223061
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.subject53C40
dc.titleCurvature integral estimates for complete hypersurfaces
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