On quasihyperbolic geodesics in banach spaces

Antti Rasila*, Jarno Talponen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We study properties of quasihyperbolic geodesics on Banach spaces. For example, we show that in a strictly convex Banach space with the Radon-Nikodym property, the quasihyperbolic geodesics are unique. We also give an example of a convex domain ω in a Banach space such that there is no geodesic between any given pair of points x, y ∈ ω. In addition, we prove that if X is a uniformly convex Banach space and its modulus of convexity is of a power type, then every geodesic of the quasihyperbolic metric, defined on a proper subdomain of X, is smooth.

Original languageEnglish
Pages (from-to)163-173
Number of pages11
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Volume39
Issue number1
DOIs
StatePublished - 2014
Externally publishedYes

Keywords

  • Banach space
  • C smoothness
  • Convex domain
  • Quasihyperbolic geodesic
  • Quasihyperbolic metric
  • Radon-Nikodym property
  • Reflexive
  • Renormings
  • Uniform convexity

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