53 citations · 332 across the 44 of their papers we have counts for
6 papers · 1 filter
Alexandrov's theorem for anisotropic capillary hypersurfaces in the half-space
Xiaohan Jia, Guofang Wang, Chao Xia +1
In this paper, we show that any embedded capillary hypersurface in the half-space with anisotropic constant mean curvature is a truncated Wulff shape. This extends Wente's result \…
Heintze-Karcher inequality and capillary hypersurfaces in a wedge
Xiaohan Jia, Guofang Wang, Chao Xia +1
In this paper, we utilize the method of Heintze-Karcher to prove a "best" version of Heintze-Karcher-type inequality for capillary hypersurfaces in the half-space or in a wedge. On…
A Minkowski-type inequality for capillary hypersurfaces in a half-space
Guofang Wang, Liangjun Weng, Chao Xia
In this article, we investigate a flow of inverse mean curvature type for capillary hypersurfaces in the half-space. We establish the global existence of solutions for this flow an…
Stability for Serrin's problem and Alexandroff's theorem in warped product manifolds
Julian Scheuer, Chao Xia
We prove quantitative versions for several results from geometric partial differential equations. Firstly, we obtain a double stability theorem for Serrin's overdetermined problem…
Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary
Guofang Wang, Liangjun Weng, Chao Xia
In this paper, we first introduce quermassintegrals for capillary hypersurfaces in the half-space. Then we solve the related isoperimetric type problems for the convex capillary hy…
A Heintze-Karcher type inequality for hypersurfaces with capillary boundary
Xiaohan Jia, Chao Xia, Xuwen Zhang
In this paper, we establish a Heintze-Karcher type inequality for hypersurfaces with capillary boundary of contact angle in a half space or a half ball, by usi…