Yimin Chen — Neckpinchhttps://neckpinch.com/authors/yimin-chen/New arXiv papers by Yimin Chen, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT A Constrained Mean Curvature Flow On Capillary Hypersurface Supported On Totally Geodesic Planehttps://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