https://neckpinch.com/authors/yuyue-chen/New arXiv papers by Yuyue Chen, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2609.18378/arxiv:2609.18378Wed, 16 Sep 2026 00:00:00 GMTYuyue Chen, Shiying Wu — We establish the eventual monotonicity of the Willmore deficit ∫_ΣH² dμ−16π along the mean curvature flow of smooth closed embedded strictly convex surfaces in ℝ³, thereby complementing Huisken's exponential convergence with an eventual monotonicity property. As a consequence, the Hawking mass is eventually nondecreasing along the contracting mean curvature flow, in contrast with the usual inclusion monotonicity expected of the Hawking mass. We also discuss totally umbilical solutions in three-dimensional space forms, where the monotonicity directions of the Willmore energy and the Hawking mass depend on the sign of the ambient sectional curvature.Mean curvature flow3-manifoldsSphere theoremsLong-time existence & convergenceGeometric inequalitiesPhysics