The inverse mean curvature flow perpendicular to the sphere

Abstract

We consider the smooth inverse mean curvature flow of strictly convex hypersurfaces with boundary embedded in ${\mathbb{R}}^{n+1},$ which are perpendicular to the unit sphere from the inside. We prove that the flow hypersurfaces converge to the embedding of a flat disk in the norm of $C^{1,\beta },$ $\beta <1.$

18 pages. Comments or suggestions are welcome

References in corpus (3)

• Curvature flows in the sphere
• Rigidity results, inverse curvature flows and Alexandrov-Fenchel type inequalities in the sphere
• Non-scale-invariant inverse curvature flows in hyperbolic space

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• A geometric inequality for convex free boundary hypersurfaces in the unit ball
• Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball
• A constrained mean curvature flow and Alexandrov-Fenchel inequalities
• The relative isoperimetric inequality for minimal submanifolds with free boundary in the Euclidean space
• A constrained mean curvature type flow for capillary boundary hypersurfaces in space forms
• Evolution of the Torsional Rigidity under Geometric Flows
• A Minkowski type inequality with free boundary in space forms
• A Constrained Mean Curvature Flow On Capillary Hypersurface Supported On Totally Geodesic Plane