On the smoothness of quasihyperbolic balls

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Tutkijat

  • Riku Klen
  • Antti Rasila
  • Jarno Talponen

Organisaatiot

  • University of Turku
  • University of Eastern Finland

Kuvaus

We investigate properties of quasihyperbolic balls and geodesics in Euclidean and Banach spaces. Our main result is that in uniformly smooth Banach spaces a quasihyperbolic ball of a convex domain is C-1-smooth. The question about the smoothness of quasihyperbolic balls is old, originating back to the discussions of Gehring and Vuorinen in 1970's. To our belief, the result is new also in the Euclidean setting. We also address some other issues involving the smoothness of quasihyperbolic balls. We introduce an interesting application of quasihyperbolic metrics to equivalent renormings of Banach spaces. Several examples and illustrations are provided.

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut439-452
Sivumäärä14
JulkaisuANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA
Vuosikerta42
Numero1
TilaJulkaistu - 2017
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 13696721