Gromov hyperbolicity, John spaces and quasihyperbolic geodesics

Zhou, Qingshan; Li, Yaxiang; Rasila, Antti

doi:10.48550/arxiv.1912.10439

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Introduction and Main Results2

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2021

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“…So Theorem 1.4 gives an improvement of [14, Theorem 1.1]. Moreover, our method of proof is more direct but simple than that of [14,Theorem 1.1].…”

Section: Introduction and Main Resultsmentioning

confidence: 91%

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Gromov hyperbolic John is quasihyperbolic John II

Zhou¹,

Ponnusamy²

2021

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In this paper, we introduce a concept of quasihyperbolic John spaces (with center) and provide a criteria to determine spaces to be quasihyperbolic John. As an application, we provide a simple proof to show that a John space with a Gromov hyperbolic quasihyperbolization is quasihyperbolic John, quantitatively. This gives an affirmative answer to an open question posed by Heinonen (Rev. Math. Iber, 1989), which has been studied by Gehring et al. (Math. Scand, 1989).

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“…So Theorem 1.4 gives an improvement of [14, Theorem 1.1]. Moreover, our method of proof is more direct but simple than that of [14,Theorem 1.1].…”

Section: Introduction and Main Resultsmentioning

confidence: 91%

“…This problem has been considered by several authors. See [1,5,9,10,14] for further details and background information. In particular, Heinonen asked in [10, Question 2] whether quasihyperbolic geodesics are cone arcs in John domains of R n which quasiconformally equivalent to the unit ball or uniform domains.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%