Willmore inequality on hypersurfaces in hyperbolic space

Abstract

In this article, we prove a geometric inequality for star-shaped and mean-convex hypersurfaces in hyperbolic space by inverse mean curvature flow. This inequality can be considered as a generalization of Willmore inequality for closed surface in hyperbolic $3$-space.

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References in corpus (1)

• Rigidity for nearly umbilical hypersurfaces in space forms