Quantitative Alexandrov theorem for capillary hypersurfaces in the half-space

2024/03/11 by Xiaohan Jia, Jia, Xiaohan, Xuwen Zhang +1 · 3 citations
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Geometric Analysis and Curvature Flows #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.2403.06597

Abstract

In this paper, we prove the quantitative version of the Alexandrov theorem for capillary hypersurfaces in the half-space, which generalizes Julin-Niinikoski's result to the capillary case. The proof is based on the quantitative analysis of the Montiel-Ros-type argument carried out in our joint works with Wang-Xia.

Cited by

• The weighted isoperimetric inequality and Sobolev inequality outside convex sets
• Existence of flat flows for volume-preserving mean curvature flow with contact angle
• Quantitative estimates for the relative isoperimetric problem and its gradient flow outside convex bodies in the plane

Related

• Alexandrov-type theorem for singular capillary CMC hypersurfaces in the half-space
• Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary II
• Alexandrov-Fenchel inequalities for capillary hypersurfaces in hyperbolic space
• A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space
• Alexandrov-Fenchel inequalities for convex anisotropic capillary hypersurfaces in the half-space