A Heintze-Karcher type inequality for hypersurfaces with capillary boundary

Abstract

In this paper, we establish a Heintze-Karcher type inequality for hypersurfaces with capillary boundary of contact angle $\theta \in (0,\frac{\pi }{2})$ in a half space or a half ball, by using solution to a mixed boundary value problem in Reilly type formula. Consequently, we give a new proof of Alexandrov type theorem for embedded capillary constant mean curvature hypersurfaces with contact angle $\theta \in (0,\frac{\pi }{2})$ in a half space or a half ball.

References in corpus (1)

• Heintze-Karcher inequality and capillary hypersurfaces in a wedge

Cited by in corpus (2)

• Rigidity and quantitative stability for partially overdetermined problems and capillary CMC hypersurfaces
• A characterization of capillary spherical caps by a partially overdetermined problem in a half ball