Observations on quasihyperbolic geometry modeled on Banach spaces

Rasila, Antti; Talponen, Jarno; Zhang, Xiaohui

doi:10.1090/proc/13989

Observations on quasihyperbolic geometry modeled on Banach spaces
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by Antti Rasila, Jarno Talponen and Xiaohui Zhang PDF

Proc. Amer. Math. Soc. 146 (2018), 3863-3873 Request permission

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.

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