Observations on quasihyperbolic geometry modeled on banach spaces

Antti Rasila, Jarno Talponen, Xiaohui Zhang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish
Pages (from-to)3863-3873
Number of pages11
JournalProceedings of the American Mathematical Society
Issue number9
StatePublished - 2018
Externally publishedYes


  • Banach space
  • Geodesic
  • Quasihyperbolic metric


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