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

Lambert, Ben; Scheuer, Julian

doi:10.1090/proc/13516

A geometric inequality for convex free boundary hypersurfaces in the unit ball
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Proc. Amer. Math. Soc. 145 (2017), 4009-4020 Request permission

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.

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