Inverse curvature flows for capillary hypersurfaces in the unit ball

TL;DR

This paper investigates inverse curvature flows for convex hypersurfaces with free boundary conditions in the unit ball, proving existence, convergence, and deriving new geometric inequalities.

Contribution

It introduces new inverse curvature flow techniques for capillary hypersurfaces and establishes Alexandrov Fenchel inequalities for weakly convex free boundary hypersurfaces.

Findings

Proved existence and convergence of inverse curvature flows for capillary hypersurfaces.

Derived Alexandrov Fenchel inequalities for weakly convex hypersurfaces with free boundary.

Established new geometric inequalities in the context of capillary hypersurfaces.

Abstract

In this paper, we study inverse curvature flows for strictly convex, capillary hypersurfaces in the unit Euclidean ball. We establish the existence and convergence results for a class of such flows. As an application, we derive a family of Alexandrov Fenchel inequalities for weakly convex hypersurfaces with free boundary.