8 papers
Uniqueness of capillary Gauss solitons
Xinqun Mei, Guofang Wang, Liangjun Weng
We prove the rigidity conjecture of [14, Conjecture 1.2] for smooth strictly convex capillary Gauss solitons in a Euclidean half-space with an acute contact angle: every such solit…
The capillary -Minkowski problem
Xinqun Mei, Guofang Wang, Liangjun Weng
This paper is a continuation of our recent work [Adv. Math. 469 (2025), Paper No. 110230] concerning the capillary Minkowski problem. We propose, in this paper, a capillary -M…
Interior estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions
Xinqun Mei, Jin Yan
In this paper, we study the interior estimates for Hessian quotient equations for , in arbitrary dimensions, under the nat…
The capillary Christoffel-Minkowski problem
Xinqun Mei, Guofang Wang, Liangjun Weng
In this article, we introduce a -th capillary area measure for capillary convex bodies in the Euclidean half-space, which serves as a boundary counterpart to the classical conce…
Prescribed curvature problem for convex capillary hypersurface
Xinqun Mei, Guofang Wang, Liangjun Weng
We study the prescribed Lp curvature problem for convex capillary hypersurfaces in the Euclidean half-space. By reducing the problem to finding a convex solution of a Hessian quoti…
The capillary Gauss curvature flow
Xinqun Mei, Guofang Wang, Liangjun Weng
In this article, we first introduce a Gauss curvature type flow for capillary hypersurfaces, which we call capillary Gauss curvature flow. We then show that the flow will shrink to…