Characterizations of generalized John domains in $\mathbb{R}^n$ via metric duality

Goldstein, Paweł; Grochulska, Zofia; Guo, Chang‐Yu; Koskela, Pekka; Nandi, Debanjan

doi:10.48550/arxiv.1710.02050

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2019

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“…This class was first considered by John [15] in the context of elasticity theory. Many characterizations of uniform and John domains can be found in the literature and the importance of these classes of domains in function theory is well established, see for example [10,18].…”

Section: Introductionmentioning

confidence: 99%

Gromov hyperbolicity, John spaces and quasihyperbolic geodesics

Zhou¹,

Li²,

Rasila³

2019

Preprint

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We show that every quasihyperbolic geodesic in a John space admitting a roughly starlike Gromov hyperbolic quasihyperbolization is a cone arc. This result provides a new approach to the elementary metric geometry question, formulated in [12, Question 2], which has been studied by Gehring, Hag, Martio and Heinonen. As an application, we obtain a simple geometric condition connecting uniformity of the space with the existence of Gromov hyperbolic quasihyperbolization.

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Section: Introductionmentioning

confidence: 99%