Observations on quasihyperbolic geometry modeled on banach spaces

Antti Rasila; Jarno Talponen; Xiaohui Zhang

doi:10.1090/proc/13989

Observations on quasihyperbolic geometry modeled on banach spaces

Antti Rasila, Jarno Talponen, Xiaohui Zhang

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Abstract

In this paper, we continue our study of the quasihyperbolic metric over Banach spaces. The main results of the paper present a criterion for smoothness of geodesics of quasihyperbolic type metrics in Banach spaces, under a Dini type condition on the weight function, which improves an earlier result of the first two authors. We also answer a question posed by the first two authors in an earlier paper with R. Klén and present results related to the question of smoothness of quasihyperbolic balls.

Original language	English
Pages (from-to)	3863-3873
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	9
DOIs	https://doi.org/10.1090/proc/13989
State	Published - 2018
Externally published	Yes

Keywords

Banach space
Geodesic
Quasihyperbolic metric

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title = "Observations on quasihyperbolic geometry modeled on banach spaces",

abstract = "In this paper, we continue our study of the quasihyperbolic metric over Banach spaces. The main results of the paper present a criterion for smoothness of geodesics of quasihyperbolic type metrics in Banach spaces, under a Dini type condition on the weight function, which improves an earlier result of the first two authors. We also answer a question posed by the first two authors in an earlier paper with R. Kl{\'e}n and present results related to the question of smoothness of quasihyperbolic balls.",

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AB - In this paper, we continue our study of the quasihyperbolic metric over Banach spaces. The main results of the paper present a criterion for smoothness of geodesics of quasihyperbolic type metrics in Banach spaces, under a Dini type condition on the weight function, which improves an earlier result of the first two authors. We also answer a question posed by the first two authors in an earlier paper with R. Klén and present results related to the question of smoothness of quasihyperbolic balls.

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KW - Geodesic

KW - Quasihyperbolic metric

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Observations on quasihyperbolic geometry modeled on banach spaces

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Keywords

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