251 citations · 827 across the 103 of their papers we have counts for
5 papers · 2 filters
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…
The visual angle metric and quasiregular maps
Gendi Wang, Matti Vuorinen
The distortion of distances between points under maps is studied. We first prove a Schwarz-type lemma for quasiregular maps of the unit disk involving the visual angle metric. Then…
Comparison theorems for hyperbolic type metrics
Oleksiy Dovgoshey, Parisa Hariri, Matti Vuorinen
The connection between several hyperbolic type metrics is studied in subdomains of the Euclidean space. In particular, a new metric is introduced and compared to the distance ratio…
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.