https://neckpinch.com/authors/xiaoshang-jin/New arXiv papers by Xiaoshang Jin, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2608.17315/arxiv:2608.17315Tue, 18 Aug 2026 00:00:00 GMTXiaoshang Jin, Yao Wan, Jie Xiao — This paper establishes sharp upper bounds for p-capacities Cap_(1<p<∞) in the hyperbolic space ℍⁿ through hyperbolic quermassintegrals and effective curvature radii. The quermassintegral comparisons involve Wₙ₋₁, Wₖ₊₁+k(n+1-k)⁻¹Wₖ₋₁, and the pair W₁mid W₂. For star-shaped, mean-convex or h-convex hypersurfaces, inverse mean curvature flow further produces curvature radii determined by L^q-averages of the normalized mean curvature and by moments of its squared hyperbolic excess. These radii convert the resulting estimates into sharp geodesic-ball comparisons for the capacity-to-area ratio. In the range p>2m+1, an interpolating radius combines the 2m-th curvature-excess radius with the L^∞ curvature scale, thereby linking the finite-moment and supremum regimes. Equality in the sharp comparisons characterizes geodesic balls.Mean curvature flowOther curvature flowsInverse mean curvature flowGeometric inequalities