Geometric properties of the Cassinian metric. Issue 10 (5th December 2016)

• Record Type: Journal Article
• Authors: Klén, Riku; Mohapatra, Manas Ranjan; Sahoo, Swadesh Kumar
• Is Part Of: Mathematische Nachrichten. Volume 290:Issue 10(2017)
• Page Start: 1531
• Page End: 1543
• Publication Date: 2016-12-05
• Subjects: Möbius transformations -- the Cassinian metric -- distortion and inclusion properties -- metric balls -- starlikeness and convexity -- 30C20 -- 30C35 -- 30F45 -- 51M10; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201600117
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract : In this paper we prove a sharp distortion property of the Cassinian metric under Möbius transformations of a punctured ball onto another punctured ball. The paper also deals with discussion on local convexity properties of the Cassinian metric balls in proper subdomains of R n . Inclusion properties of the Cassinian metric balls with other hyperbolic‐type metric balls are also investigated. In particular, several conjectures are also stated in response to sharpness of the inclusion relations.