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arXiv · 2207.08039

Further Study on Domains and Quasihyperbolic Distances

Shusen Ding·Dylan Helliwell·Gavin Pandya·Arya Yae
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Abstract

We establish constructive geometric tools for determining when a domain is $L^s$-averaging and obtain upper and lower bounds for the $L^s$-integrals of the quasihyperbolic distance. We also construct examples which are helpful to understand our geometric tools and the relationship between $p$-Poincar\'{e} domains and $L^s$-averaging domains. Finally, finite unions of $L^s(\mu)$-averaging domains are explored.

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Shusen Ding, Dylan Helliwell, Gavin Pandya, Arya Yae. 2022-07-16. Further Study on Domains and Quasihyperbolic Distances. https://arxiv.org/abs/2207.08039

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