On the smoothness of quasihyperbolic balls

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Standard

On the smoothness of quasihyperbolic balls. / Klen, Riku; Rasila, Antti; Talponen, Jarno.

julkaisussa: ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, Vuosikerta 42, Nro 1, 2017, s. 439-452.

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Harvard

APA

Vancouver

Author

Klen, Riku ; Rasila, Antti ; Talponen, Jarno. / On the smoothness of quasihyperbolic balls. Julkaisussa: ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA. 2017 ; Vuosikerta 42, Nro 1. Sivut 439-452.

Bibtex - Lataa

@article{9f994a3c74054dc18f14750163f85f51,
title = "On the smoothness of quasihyperbolic balls",
abstract = "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.",
keywords = "Quasihyperbolic metric, geodesics, uniqueness, smoothness, convexity, renorming, BANACH-SPACES, CONVEXITY PROPERTIES, UNIFORM DOMAINS, GEODESICS",
author = "Riku Klen and Antti Rasila and Jarno Talponen",
year = "2017",
doi = "10.5186/ansfm.2017.4226",
language = "English",
volume = "42",
pages = "439--452",
journal = "ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA",
issn = "1239-629X",
number = "1",

}

RIS - Lataa

TY - JOUR

T1 - On the smoothness of quasihyperbolic balls

AU - Klen, Riku

AU - Rasila, Antti

AU - Talponen, Jarno

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Quasihyperbolic metric

KW - geodesics

KW - uniqueness

KW - smoothness

KW - convexity

KW - renorming

KW - BANACH-SPACES

KW - CONVEXITY PROPERTIES

KW - UNIFORM DOMAINS

KW - GEODESICS

U2 - 10.5186/ansfm.2017.4226

DO - 10.5186/ansfm.2017.4226

M3 - Article

VL - 42

SP - 439

EP - 452

JO - ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA

JF - ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA

SN - 1239-629X

IS - 1

ER -

ID: 13696721