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

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.

19 pages. All comments are welcome

References in corpus (4)

• A geometric inequality on hypersurface in hyperbolic space
• An Alexandrov-Fenchel-type inequality in hyperbolic space with an application to a Penrose inequality
• Curvature flows in the sphere
• A Minkowski-type inequality for convex surfaces in the hyperbolic 3-space

Cited by in corpus (10)

• Locally constrained inverse curvature flows
• On inverse mean curvature flow in Schwarzschild space and Kottler space
• Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary
• A geometric inequality for convex free boundary hypersurfaces in the unit ball
• Inverse curvature flows in Riemannian warped products
• The Minkowski inequality in de Sitter space
• On an inverse curvature flow in two-dimensional space forms
• Minkowski inequalities and constrained inverse curvature flows in warped spaces
• A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space
• Blaschke-Santaló type inequalities and quermassintegral inequalities in space forms