Local convexity properties of balls in Apollonian and Seittenranta’s metrics-Reference-Cited by-同舟云学术

Local convexity properties of balls in Apollonian and Seittenranta’s metrics

Published:2013-09-10 Issue:10 Volume:17 Page:133-144
ISSN:1088-4173
Container-title:Conformal Geometry and Dynamics of the American Mathematical Society
language:en
Short-container-title:Conform. Geom. Dyn.

Author:

Klén Riku

Abstract

We consider local convexity properties of balls in the Apollonian and Seittenranta’s metrics. Balls in the Apollonian metric are considered in the twice punctured space and starlike domains. Balls in Seittenranta’s metric are considered in the twice punctured space and in the punctured ball.

Publisher

American Mathematical Society (AMS)

Subject

Geometry and Topology

Link

http://www.ams.org/ecgd/2013-17-10/S1088-4173-2013-00257-9/S1088-4173-2013-00257-9.pdf

Reference23 articles.

1. [Ba] D. Barbilian, Einordnung von Lobayschewsky’s Massenbestimmung in einer gewissen allgemeinen Metrik der Jordansche Bereiche. Casopis Mathematiky a Fysiky 64 (1934–35), 182–183.

2. The Apollonian metric of a domain in 𝑅ⁿ;Beardon, A. F.,1998

3. The Apollonian metric and quasiconformal mappings;Gehring, F. W.,2000

4. The Apollonian metric: uniformity and quasiconvexity;Hästö, Peter A.;Ann. Acad. Sci. Fenn. Math.,2003

5. The Apollonian metric: quasi-isotropy and Seittenranta’s metric;Hästö, Peter A.;Comput. Methods Funct. Theory,2004

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Growth of Some Hyperbolic Type Distances and Starlikeness of Metric Balls;Bulletin of the Malaysian Mathematical Sciences Society;2023-03-23

2. Local Convexity of Balls;Springer Monographs in Mathematics;2020

3. Local convexity of metric balls;Monatshefte für Mathematik;2017-12-02

4. Hyperbolic Type Distances in Starlike Domains;Results in Mathematics;2017-01-06

5. Geometric properties of the Cassinian metric;Mathematische Nachrichten;2016-12-05