A geometric inequality for convex free boundary hypersurfaces in the unit ball

TL;DR

This paper establishes a new geometric inequality involving Willmore energy for convex hypersurfaces with free boundary in the unit ball, using inverse mean curvature flow techniques.

Contribution

It introduces a novel application of inverse mean curvature flow to derive inequalities for convex free boundary hypersurfaces in the unit ball.

Findings

Proves a geometric inequality involving Willmore energy for convex hypersurfaces.

Utilizes inverse mean curvature flow with free boundary conditions.

Results apply to hypersurfaces of dimension n ≥ 3.

Abstract

We use the inverse mean curvature flow with a free boundary perpendicular to the sphere to prove a geometric inequality involving the Willmore energy for convex hypersurfaces of dimension $n\geq 3$ with boundary on the sphere.