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ON THE SMOOTHNESS OF QUASIHYPERBOLIC BALLS
Tekijät: Riku Klén, Antti Rasila, Jarno Talponen
Kustantaja: SUOMALAINEN TIEDEAKATEMIA
Julkaisuvuosi: 2017
Journal: Annales Academiae Scientiarum Fennicae. Mathematica
Tietokannassa oleva lehden nimi: ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA
Lehden akronyymi: ANN ACAD SCI FENN-M
Vuosikerta: 42
Numero: 1
Aloitussivu: 439
Lopetussivu: 452
Sivujen määrä: 14
ISSN: 1239-629X
DOI: https://doi.org/10.5186/aasfm.2017.4226
Verkko-osoite: http://www.acadsci.fi/mathematica/Vol42/vol42pp439-452.pdf
Tiivistelmä
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.
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.
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