33 citations · 140 across the 29 of their papers we have counts for
6 papers · 1 filter
Condenser capacity and hyperbolic diameter
Mohamed M. S. Nasser, Oona Rainio, Matti Vuorinen
Given a compact connected set in the unit disk , we give a new upper bound for the conformal capacity of the condenser in terms of the hyp…
Intrinsic quasi-metrics
Oona Rainio
The point pair function defined in a domain is shown to be a quasi-metric and its other properties are studied. For a convex domain $G\subsetneq\mat…
Introducing a new intrinsic metric
Oona Rainio, Matti Vuorinen
A new intrinsic metric called -metric is introduced. Several sharp inequalities between this metric and the most common hyperbolic type metrics are proven for various domains $G…
Triangular ratio metric in the unit disk
Oona Rainio, Matti Vuorinen
The triangular ratio metric is studied in a domain , . Several sharp bounds are proven for this metric, especially, in the case where the domain is…
Intrinsic geometry and boundary structure of plane domains
Oona Rainio, Toshiyuki Sugawa, Matti Vuorinen
For a non-empty compact set in a proper subdomain of the complex plane, we denote the diameter of and the distance from to the boundary of by and $d(E,\p…
Triangular ratio metric under quasiconformal mappings in sector domains
Oona Rainio, Matti Vuorinen
Hyperbolic metric and different hyperbolic type metrics are studied in open sector domains of the complex plane. Several sharp inequalities are proven for them. Our main result des…