45 citations · 116 across the 18 of their papers we have counts for
20 papers
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…
New trigonometric and hyperbolic inequalities
Barkat Ali Bhayo, Riku Klén, József Sándor
The aim of this paper is to prove new trigonometric and hyperbolic inequalities, which constitute among others refinements or analogs of famous Cusa-Huygens, Wu-Srivastava, and rel…
On isometries of conformally invariant metric
Riku Klén, Matti Vuorinen, Xiaohui Zhang
We prove that isometries in a conformally invariant metric of a general domain are quasiconformal. In the particular case of the punctured space, we prove that isometries in this m…
On smoothness of quasihyperbolic balls
Riku Klén, Antti Rasila, Jarno Talponen
We investigate properties of quasihyperbolic balls and geodesics in Euclidean and Banach spaces. Our main result is that in uniformly smooth Banach spaces a quasihyperbolic ball of…
Lipschitz conditions, triangular ratio metric, and quasiconformal maps
Jiaolong Chen, Parisa Hariri, Riku Klén +1
The triangular ratio metric is studied in subdomains of the complex plane and Euclidean -space. Various inequalities are proven for it. The main results deal with the behavior o…