Willmore inequality on hypersurfaces in hyperbolic space

TL;DR

This paper establishes a new geometric inequality for certain hypersurfaces in hyperbolic space using inverse mean curvature flow, extending the classical Willmore inequality to higher dimensions.

Contribution

It introduces a generalized Willmore inequality for star-shaped, mean-convex hypersurfaces in hyperbolic space via inverse mean curvature flow.

Findings

Proved a geometric inequality for hypersurfaces in hyperbolic space.

Generalized Willmore inequality to higher dimensions.

Applicable to star-shaped, mean-convex hypersurfaces.

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.