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

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 $n\ge 3$ with boundary on the sphere.

9 pages. Comments are welcome

References in corpus (5)

• A geometric inequality on hypersurface in hyperbolic space
• Curvature flows in the sphere
• A New Monotone Quantity along the Inverse Mean Curvature Flow in ${\mathbb{R}}^n$
• Alexandrov-Fenchel type inequalities for convex hypersurfaces in hyperbolic space and in sphere
• The inverse mean curvature flow perpendicular to the sphere

Cited by in corpus (9)

• Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball
• A mean curvature type flow with capillary boundary in a unit ball
• Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary
• Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball
• A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space
• On the mean curvature type flow for convex capillary hypersurfaces in the ball
• Weighted Hsiung-Minkowski formulas and rigidity of umbilical hypersurfaces
• A constrained mean curvature type flow for capillary boundary hypersurfaces in space forms
• Capacity inequalities and rigidity of cornered/conical manifolds