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arXiv · 2502.13666

Essential $p$-capacity-volume estimates for rotationally symmetric manifolds

Xiaoshang Jin·Jie Xiao
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Abstract

Given $p\in [1,\infty]$, this article presents the novel basic volumetric estimates for the relative $p$-capacities with their applications to finding not only the sharp weak $(p,q)$-imbeddings but also the precise lower bounds of the principal $p$-frequencies, which principally live in the rotationally symmetric manifolds.

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Xiaoshang Jin, Jie Xiao. 2025-02-19. Essential $p$-capacity-volume estimates for rotationally symmetric manifolds. https://arxiv.org/abs/2502.13666

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