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arXiv · 2608.17315

Sharp $p$-Capacity Estimates via Quermassintegrals in Hyperbolic Space

Xiaoshang Jin·Yao Wan·Jie Xiao
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Abstract

This paper establishes sharp upper bounds for $p$-capacities $\mathrm{Cap}_{1 2m+1$, an interpolating radius combines the $2m$-th curvature-excess radius with the $L^\infty$ curvature scale, thereby linking the finite-moment and supremum regimes. Equality in the sharp comparisons characterizes geodesic balls.

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Xiaoshang Jin, Yao Wan, Jie Xiao. 2026-08-18. Sharp $p$-Capacity Estimates via Quermassintegrals in Hyperbolic Space. https://arxiv.org/abs/2608.17315

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