Gromov hyperbolic John is quasihyperbolic John I

Qingshan Zhou; Saminathan Ponnusamy

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arXiv · 2111.13797

Gromov hyperbolic John is quasihyperbolic John I

Qingshan Zhou·Saminathan Ponnusamy

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Abstract

In this paper, we introduce a concept of quasihyperbolic John spaces and provide a necessary and sufficient condition for a space to be quasihyperbolic John. Using this criteria, we exhibit a simple proof to show that a John space with a Gromov hyperbolic quasihyperbolization is quasihyperbolic John, quantitatively. This answers affirmatively to an open question proposed by Heinonen (Rev.~Math.~Iber, 1989), which was studied by Gehring et al. (Math.~Scand, 1989). As a tool, we study its connection between several geometric conditions.

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Qingshan Zhou, Saminathan Ponnusamy. 2021-11-27. Gromov hyperbolic John is quasihyperbolic John I. https://arxiv.org/abs/2111.13797

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