45 citations · 116 across the 18 of their papers we have counts for
10 papers · 1 filter
Ptolemy constant and uniformity
Eero Harmaala, Riku Klén
We study Ptolemy constant and uniformity constant in various plane domains including triangles, quadrilaterals and ellipses.
Geometric properties of the Cassinian metric
Riku Klén, Manas Ranjan Mohapatra, Swadesh Kumar Sahoo
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 d…
Balls in the triangular ratio metric
Sami Hokuni, Riku Klén, Yaxiang Li +1
We consider the triangular ratio metric and estimate the radius of convexity for balls in some special domains and prove the inclusion relations of metric balls defined by the tria…
Subdomain geometry of hyperbolic type metrics
Riku Klén, Yaxiang Li, Matti Vuorinen
Given a domain $G \subsetneq \Rn$ we study the quasihyperbolic and the distance ratio metrics of and their connection to the corresponding metrics of a subdomain .…
Volume growth of quasihyperbolic balls
Xiaohui Zhang, Riku Klén, Ville Suomala +1
The purpose of this paper is to study the notion of the quasihyperbolic volume and to find growth estimates for the quasihyperbolic volume of balls in a domain $G \subset {\mathbb…
Local convexity properties of Apollonian and Seittenranta's metric balls
Riku Klén
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 starlik…