Inverse curvature flows for capillary hypersurfaces in the unit ball

2025/07/16 by Shujing Pan, Bo Yang, Pan, Shujing +1
Mathematics · #35K93 #52A40 #53C21 #53C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2507.12097

openalex publication_date 2025/07/16 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

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.

Citations

• Dual flows in hyperbolic space and de Sitter space

Related

• Alexandrov-Fenchel inequalities for capillary hypersurfaces in hyperbolic space
• A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space
• Locally constrained inverse curvature flow and Alexandrov-Fenchel type inequalities in de Sitter space
• Inverse Gauss curvature flows with free boundaries in a cone
• Free boundary flows by powers of the Gauss curvature in the unit ball