https://neckpinch.com/authors/changwei-xiong/New arXiv papers by Changwei Xiong, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2306.09009/arxiv:2306.09009Thu, 15 Jun 2023 00:00:00 GMTHaizhong Li, Ruixuan Li, Changwei Xiong — We derive various sharp upper bounds for the p-capacity of a smooth compact set K in the hyperbolic space ℍⁿ and the Euclidean space ℝⁿ. Firstly, using the inverse mean curvature flow, for the mean convex and star-shaped set K in ℍⁿ, we obtain sharp upper bounds for the p-capacity Capₚ(K) in three cases: (1) n≥ 2 and p=2, (2) n=2 and p≥ 3, (3) n=3 and 1<p≤ 3; Using the unit-speed normal flow, we prove a sharp upper bound for Capₚ(K) of a convex set K in ℍⁿ for n≥ 2 and p>1. Secondly, for the compact set K in ℝ³, using the weak inverse mean curvature flow, we get a sharp upper bound for the p-capacity (1<p<3) of the set K with connected boundary; Using the inverse anisotropic mean curvature flow, we deduce a sharp upper bound for the anisotropic p-capacity (1<p<3) of an F-mean convex and star-shaped set K in ℝ³.Mean curvature flowOther curvature flowsInverse mean curvature flowAnisotropic & nonlocal flows