Rigidity and quantitative stability for partially overdetermined problems and capillary CMC hypersurfaces

TL;DR

This paper establishes rigidity and quantitative stability results for partially overdetermined problems and capillary constant mean curvature hypersurfaces in the half-space, characterizing spherical caps and their stability.

Contribution

It provides new rigidity theorems and stability estimates for capillary hypersurfaces and overdetermined problems in the half-space, extending classical results.

Findings

Rigidity characterization of capillary spherical caps.

Quantitative stability estimates for almost constant mean curvature hypersurfaces.

Extension of Serrin-type overdetermined problem results.

Abstract

In this paper, we first prove a rigidity result for a Serrin-type partially overdetermined problem in the half-space, which gives a characterization of capillary spherical caps by the overdetermined problem. In the second part, we prove quantitative stability results for the Serrin-type partially overdetermined problem, as well as capillary almost constant mean curvature hypersurfaces in the half-space.