17 citations · 82 across the 19 of their papers we have counts for
20 papers
Quermassintegral inequalities for capillary hypersurfaces in a horoball
Jinyu Guo, Liangjun Weng
In this paper, we study the quermassintegral inequalities for capillary hypersurfaces in a horoball in hyperbolic space. We construct a locally constrained nonlinear curvature flow…
Uniqueness of capillary Gauss solitons
Xinqun Mei, Guofang Wang, Liangjun Weng
We prove the rigidity conjecture of [16, 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 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 address the prescribed curvature problem for convex capillary hypersurfaces in the Euclidean half-space. Using the support function, we formulate the problem as a Hessian…
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…
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…
Convex capillary hypersurfaces of prescribed curvature problem
Xinqun Mei, Guofang Wang, Liangjun Weng
In this paper, we study the prescribed -th Weingarten curvature problem for convex capillary hypersurfaces in . This problem naturally extends the…
A fully nonlinear locally constrained curvature flow for capillary hypersurface
Xinqun Mei, Liangjun Weng
In this article, we study a locally constrained fully nonlinear curvature flow for convex capillary hypersurfaces in half-space. We prove that the flow preserves the convexity, exi…
Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary II
Xinqun Mei, Guofang Wang, Liangjun Weng +1
In this paper, we provide an affirmative answer to [16, Conjecture 1.5] on the Alexandrov-Fenchel inequality for quermassintegrals for convex capillary hypersurfaces in the Euclide…
Alexandrov-Fenchel inequalities for capillary hypersurfaces in hyperbolic space
Xinqun Mei, Liangjun Weng
In this article, we first introduce the quermassintegrals for compact hypersurfaces with capillary boundaries in hyperbolic space from a variational viewpoint, and then we solve an…
Hypersurfaces with capillary boundary evolving by volume preserving power mean curvature flow
Carlo Sinestrari, Liangjun Weng
In this paper, we introduce a volume- or area-preserving curvature flow for hypersurfaces with capillary boundary in the half-space, with speed given by a positive power of the mea…
Prescribed quotient curvature problem and related eigenvalue problem
Xinqun Mei, Guofang Wang, Liangjun Weng
In this paper, we investigate the existence of admissible (and strictly convex) smooth solutions to the prescribed quotient type curvature problem with . For cases where…
A constrained mean curvature type flow for capillary boundary hypersurfaces in space forms
Xinqun Mei, Liangjun Weng
In this paper, we introduce a new constrained mean curvature type flow for capillary boundary hypersurfaces in space forms. We show the flow exists for all time and converges globa…
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…
A constrained mean curvature flow and Alexandrov-Fenchel inequalities
Xinqun Mei, Guofang Wang, Liangjun Weng
In this article, we study a locally constrained mean curvature flow for star-shaped hypersurfaces with capillary boundary in the half-space. We prove its long-time existence and th…
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…
Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball
Liangjun Weng, Chao Xia
In this paper, we first introduce the quermassintegrals for convex hypersurfaces with capillary boundary in the unit Euclidean ball and derive its first variatio…
The relative isoperimetric inequality for minimal submanifolds with free boundary in the Euclidean space
Lei Liu, Guofang Wang, Liangjun Weng
In this paper, we mainly consider the relative isoperimetric inequalities for minimal submanifolds with free boundary. We first generalize ideas of restricted normal cones introduc…
A mean curvature type flow with capillary boundary in a unit ball
Guofang Wang, Liangjun Weng
In this paper, we study a mean curvature type flow with capillary boundary in the unit ball. Our flow preserves the volume of the bounded domain enclosed by the hypersurface, and m…
Lagrangian surfaces with Legendrian boundary
Mingyan Li, Guofang Wang, Liangjun Weng
In this note, we first introduce a boundary problem for Lagrangian submanifolds, analogous to the problem for free boundary hypersurfaces and capillary hypersurfaces. Then we prese…