17 citations · 55 across the 20 of their papers we have counts for
20 papers
Regularity of branched stable minimal immersed hypersurfaces
Gaoming Wang, Xuwen Zhang
We establish a sharp bound on the Hausdorff dimension of the non-branch singular set of branched stable minimal immersed hypersurfaces whose singular sets have locally finite $\mat…
Regularity of stable capillary minimal hypersurfaces
Gaoming Wang, Xuwen Zhang
We develop a regularity and compactness theory for stable capillary minimal hypersurfaces in the half-space with contact angle and dimension $n \geq…
A half-space Liouville theorem for anisotropic minimal graph with free boundary
Guofang Wang, Wei Wei, Chao Xia +1
In this paper we prove the following Liouville-type theorem: any anisotropic minimal graph with free boundary in the half-space must be flat, provided that the graph function has a…
Half-space Liouville-type theorems for minimal graphs with capillary boundary
Guofang Wang, Wei Wei, Xuwen Zhang
In this paper, we prove two Liouville-type theorems for capillary minimal graph over . First, if has linear growth, then for and for any , or…
Varifolds with capillary boundary
Guofang Wang, Xuwen Zhang
In this paper we introduce and study a new class of varifolds in of arbitrary dimensions and co-dimensions, which satisfy a Neumann-type boundary condition chara…
Monotonicity Formulas for Capillary Surfaces
Guofang Wang, Chao Xia, Xuwen Zhang
In this paper, we establish monotonicity formulas for capillary surfaces in the half-space and in the unit ball and extend the result of Volkmann (C…
Willmore-type inequality in unbounded convex sets
Xiaohan Jia, Guofang Wang, Chao Xia +1
In this paper we prove the following Willmore-type inequality: On an unbounded closed convex set , for any embedded hypersurface w…
Quantitative Alexandrov theorem for capillary hypersurfaces in the half-space
Xiaohan Jia, Xuwen Zhang
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 capilla…
Rigidity and quantitative stability for partially overdetermined problems and capillary CMC hypersurfaces
Xiaohan Jia, Zheng Lu, Chao Xia +1
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…
Heintze-Karcher inequality for anisotropic free boundary hypersurfaces in convex domains
Xiaohan Jia, Guofang Wang, Chao Xia +1
In this paper, we prove an optimal Heintze-Karcher-type inequality for anisotropic free boundary hypersurfaces in general convex domains. The equality is achieved for anisotropic f…
A characterization of capillary spherical caps by a partially overdetermined problem in a half ball
Xiaohan Jia, Zheng Lu, Chao Xia +1
In this note, we study a Serrin-type partially overdetermined problem proposed by Guo-Xia (Calc. Var. Partial Differential Equations 58: no. 160, 2019. https://doi.org/10.1007/s005…
Stability of the Wulff shape with respect to anisotropic curvature functionals
Julian Scheuer, Xuwen Zhang
For a function which foliates a one-sided neighbourhood of a closed hypersurface , we give an estimate of the distance of to a Wulff shape in terms of the -norm o…
Alexandrov-type theorem for singular capillary CMC hypersurfaces in the half-space
Chao Xia, Xuwen Zhang
In this paper, we consider the classification problem for critical points of relative isoperimetric-type problem in the half-space. Under certain regularity assumption, we prove an…
Capillary Schwarz symmetrization in the half-space
Zheng Lu, Chao Xia, Xuwen Zhang
In this paper, we introduce a notion of capillary Schwarz symmetrization in the half-space. It can be viewed as the counterpart of the classical Schwarz symmetrization in the frame…
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 boundary maximum principle for stationary pairs of varifolds with fixed contact angle
Xuwen Zhang
In this note, we establish a boundary maximum principle for a class of stationary pairs of varifolds satisfying a fixed contact angle condition in any compact Riemannian manifold w…
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…
-rectifiability and Heintze-Karcher inequality on
Xuwen Zhang
In this paper, by isometrically embedding into , and using nonlinear analysis on the codimension-2 graphs, we will show…
Uniqueness for volume-constraint local energy-minimizing sets in a half-space or a ball
Chao Xia, Xuwen Zhang
In this paper, we prove a Poincaré-type inequality for any set of finite perimeter which is stable with respect to the free energy among volume-preserving perturbation, provided th…