https://neckpinch.com/authors/xuan-yao/New arXiv papers by Xuan Yao, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2305.19784/arxiv:2305.19784Wed, 31 May 2023 00:00:00 GMTLiam Mazurowski, Xuan Yao — Consider a complete asymptotically flat 3-manifold M with non-negative scalar curvature and non-empty minimal boundary Σ. Fix a number 1 < p < 3. We derive monotone quantities for p-harmonic functions on M which become constant on Schwarzschild. These monotonicity formulas imply a sharp mass-capacity estimate relating the ADM mass of M with the p-capacity of Σ in M, which was first proved by Xiao using weak inverse mean curvature flow.Mean curvature flowOther curvature flowsInverse mean curvature flow3-manifoldsScalar curvatureBoundaries & non-compactGeometric inequalitiesPhysics