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

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.

References in corpus (7)

• Bubbling with $L^2$-almost constant mean curvature and an Alexandrov-type theorem for crystals
• Alexandrov's theorem for anisotropic capillary hypersurfaces in the half-space
• Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary
• Heintze-Karcher inequality and capillary hypersurfaces in a wedge
• Absence of bubbling phenomena for non convex anisotropic nearly umbilical and quasi Einstein hypersurfaces
• Stability for Serrin's problem and Alexandroff's theorem in warped product manifolds
• A Heintze-Karcher type inequality for hypersurfaces with capillary boundary