https://neckpinch.com/authors/xiaoxiang-chai/New arXiv papers by Xiaoxiang Chai, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2405.06934/arxiv:2405.06934Sat, 11 May 2024 00:00:00 GMTXiaoxiang Chai, Yimin Chen — We prove a new Minkowski type formula for capillary hypersurfaces supported on totally geodesic hyperplanes in hyperbolic space. It leads to a volume-preserving flow starting from a star-shaped initial hypersurface. We prove the long-time existence of the flow and its uniform convergence to a θ-totally umbilical cap. Additionally, we establish that a θ-totally umbilical cap is an energy minimizer for a given enclosed volume.Mean curvature flowVolume-preserving & constrained flowsFree boundary & capillaryLong-time existence & convergence https://neckpinch.com/papers/2203.08467/arxiv:2203.08467Wed, 16 Mar 2022 00:00:00 GMTXiaoxiang Chai — We study inverse mean curvature flow with free boundary supported on geodesic spheres in hyperbolic space. Starting from any convex hypersurface inside a geodesic ball with a free boundary, the flow converges to a totally geodesic disk in finite time. Using the convergence result, we show a Willmore type inequality.Mean curvature flowOther curvature flowsInverse mean curvature flowSingularitiesFree boundary & capillary