A1 Refereed original research article in a scientific journal
Geometric properties of the Cassinian metric
Authors: Riku Klén, Manas Ranjan Mohapatra, Swadesh Kumar Sahoo
Publisher: Wiley - V C H Verlag GmbH & Co. KGaA
Publication year: 2017
Journal: Mathematical News / Mathematische Nachrichten
Volume: 290
Issue: 10
First page : 1531
Last page: 1543
Number of pages: 13
ISSN: 0025-584X
eISSN: 1522-2616
DOI: https://doi.org/10.1002/mana.201600117
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 
.
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.
