ON QUASIHYPERBOLIC GEODESICS IN BANACH SPACES

被引：20

作者：

Rasila, Antti ^{[1
,2
]}

Talponen, Jarno ^{[3
]}

机构：

[1] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China

[2] Aalto Univ, Inst Math, FI-00076 Aalto, Finland

[3] Univ Eastern Finland, Dept Math & Phys, FI-80101 Joensuu, Finland

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2014年 / 39卷 / 01期

关键词：

Quasihyperbolic metric; quasihyperbolic geodesic; uniform convexity; Banach space; C-1; smoothness; renormings; reflexive; Radon-Nikodym property; convex domain; FREE QUASICONFORMALITY; CONVEXITY PROPERTIES; UNIFORM DOMAINS; GEOMETRY; BALLS;

D O I：

10.5186/aasfm.2014.3924

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Omega in a Banach space such that there is no geodesic between any given pair of points x, y is an element of Omega. 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.

引用

页码：163 / 173

页数：11

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