38 citations · 82 across the 9 of their papers we have counts for
8 papers · 1 filter
Hyperbolic type distances in starlike domains
Riku Klén
We study the growth of hyperbolic type distances in starlike domains. We derive estimates for various hyperbolic type distances and consider the asymptotic sharpness of the estimat…
Local convexity of metric balls
Parisa Hariri, Riku Klén, Matti Vuorinen
We study local convexity properties of the triangular ratio metric balls in proper subdomains of the real coordinate space. We also study inclusion properties of the visual angle m…
Geometric properties of -uniform domains
Peter Hästö, Riku Klén, Swadesh Kumar Sahoo +1
We consider proper subdomains of and their images under quasiconformal mappings of . We compare the distance ratio metrics of and…
Some remarks on the Cassinian metric
Parisa Hariri, Riku Klen, Matti Vuorinen +1
Some sharp inequalities between the triangular ratio metric and the Cassinian metric are proved in the unit ball.
The visual angle metric and Möbius transformations
Riku Klén, Henri Lindén, Matti Vuorinen +1
A new similarity invariant metric is introduced. The visual angle metric is defined on a domain $G\subsetneq\Rn$ whose boundary is not a proper subset of a line. We fin…
Close-to-convexity of quasihyperbolic and -metric balls
Riku Klén
We will consider close-to-convexity of the metric balls defined by the quasihyperbolic metric and the -metric. We will show that the -metric balls with small radii are close-…
Local Convexity Properties of Quasihyperbolic Balls in Punctured Space
Riku Klen
This paper deals with local convexity properties of the quasihyperbolic metric in the punctured space. We consider convexity and starlikeness of quasihyperbolic balls.
Local Convexity Properties of j-metric Balls
Riku Klen
This paper deals with local convexity properties of the j-metric. We consider convexity and starlikeness of the j-metric balls in convex, starlike and general subdomains of R^n.