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arXiv · 1308.5544

Alexandrov-Fenchel type inequalities for convex hypersurfaces in hyperbolic space and in sphere

Yong Wei·Changwei Xiong
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Abstract

In this paper, firstly, inspired by Natário's recent work \cite{Na}, we use the isoperimetric inequality to derive some Alexandrov-Fenchel type inequalities for closed convex hypersurfaces in the hyperbolic space $\H^{n+1}$ and in the sphere $\SS^{n+1}$. We also get the rigidity in the spherical case. Secondly, we use the inverse mean curvature flow in sphere \cite{gerh,Mak-Sch} to prove an optimal Sobolev type inequality for closed convex hypersurfaces in the sphere.

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Yong Wei, Changwei Xiong. 2013-08-26. Alexandrov-Fenchel type inequalities for convex hypersurfaces in hyperbolic space and in sphere. https://doi.org/10.2140/pjm.2015.277.219

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