https://neckpinch.com/authors/chao-xia/New arXiv papers by Chao Xia, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2206.04639arxiv:2206.04639Thu, 09 Jun 2022 00:00:00 GMTGuofang 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 hypersurfaces and obtain the corresponding Alexandrov-Fenchel inequalities. In order to prove these results, we construct a new locally constrained curvature flow and prove that the flow converges globally to a spherical cap.Other curvature flowsVolume-preserving & constrained flowsFree boundary & capillaryGeometric inequalities https://arxiv.org/abs/2111.05773arxiv:2111.05773Wed, 10 Nov 2021 00:00:00 GMTLiangjun Weng, Chao Xia — In this paper, we first introduce the quermassintegrals for convex hypersurfaces with capillary boundary in the unit Euclidean ball Bⁿ⁺¹ and derive its first variational formula. Then by using a locally constrained nonlinear curvature flow, which preserves the n-th quermassintegral and non-decreases the k-th quermassintegral, we obtain the Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in Bⁿ⁺¹. This generalizes the result in for convex hypersurfaces with free boundary in Bⁿ⁺¹.Other curvature flowsVolume-preserving & constrained flowsFree boundary & capillaryGeometric inequalities