251 citations · 827 across the 103 of their papers we have counts for
9 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…
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…
Isoperimetric properties of condenser capacity
Mohamed M. S. Nasser, Matti Vuorinen
For compact subsets of the unit disk we study the capacity of the condenser by means of set functionals defined in terms of hyperbolic…
Conformally invariant complete metrics
Toshiyuki Sugawa, Matti Vuorinen, Tanran Zhang
For a domain in the one-point compactification of , we characterize the completeness of the mod…
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…
Teichmüller's theorem in higher dimensions and its applications
Anatoly Golberg, Toshiyuki Sugawa, Matti Vuorinen
For a given ring (domain) in we discuss whether its boundary components can be separated by an annular ring with modulus nearly equal to that of the given…