https://neckpinch.com/authors/xinqun-mei/New arXiv papers by Xinqun Mei, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2608.22494arxiv:2608.22494Sun, 23 Aug 2026 00:00:00 GMTXinqun 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 soliton is a spherical cap. Combined with our previous convergence result for the capillary Gauss curvature flow [16, Theorem 1.1], it follows that the flow starting from a strictly convex capillary hypersurface with an acute contact angle converges to a capillary spherical cap, after a suitable rescaling.Other curvature flowsGauss curvature flowStability & uniquenessFree boundary & capillary https://arxiv.org/abs/2506.09840arxiv:2506.09840Wed, 11 Jun 2025 00:00:00 GMTXinqun 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 a point in finite time. This is a capillary counterpart (or Robin boundary counterpart) of Firey's problem studied in [Mathematika 21 (1974), pp. 1-11] and Tso [Comm. Pure Appl. Math. 38 (1985), no. 6, 867-882]. Finally, we prove that its normalized flow converges to a soliton. This is a capillary counterpart of the result of Guan and Ni in [J. Eur. Math. Soc. 19 (2017), no. 12, 3735-3761]. The classification of solitons remains an open conjecture.Other curvature flowsGauss curvature flowSingularitiesFree boundary & capillary https://arxiv.org/abs/2408.13815arxiv:2408.13815Sun, 25 Aug 2024 00:00:00 GMTXinqun 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, exists for all time, and converges smoothly to a spherical cap. This can be viewed as the fully nonlinear counterpart of the result in. As a byproduct, a high-order capillary isoperimetric ratio (1.6) evolves monotonically along this flow, which yields a class of the Alexandrov-Fenchel inequalities.Other curvature flowsVolume-preserving & constrained flowsFree boundary & capillaryLong-time existence & convergenceGeometric inequalities https://arxiv.org/abs/2406.07304arxiv:2406.07304Tue, 11 Jun 2024 00:00:00 GMTXinqun 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 isoperimetric type problem in hyperbolic space. By constructing a new locally constrained inverse curvature flow, we obtain the Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in hyperbolic space. This generalizes a theorem of Brendle-Guan-Li for convex closed hypersurfaces in hyperbolic space.Other curvature flowsInverse mean curvature flowVolume-preserving & constrained flowsFree boundary & capillaryGeometric inequalities https://arxiv.org/abs/2209.13463arxiv:2209.13463Tue, 27 Sep 2022 00:00:00 GMTXinqun 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 the global convergence to a spherical cap. Furthermore, the capillary quermassintegrals defined in evolve monotonically along the flow, and hence we establish a class of new Alexandrov-Fenchel inequalities for convex hypersurfaces with capillary boundary in the half-space.Mean curvature flowVolume-preserving & constrained flowsFree boundary & capillaryLong-time existence & convergenceGeometric inequalities