33 citations · 140 across the 29 of their papers we have counts for
18 papers · 1 filter
Inequalities for a new hyperbolic type metric
Oona Rainio
We study a new hyperbolic type metric recently introduced by Song and Wang. We present formulas for it in the upper half-space and the unit ball domains and find its sharp inequali…
Visual angle metric in the upper half plane
Masayo Fujimura, Oona Rainio, Matti Vuorinen
We prove an identity which connects the visual angle metric and the hyperbolic metric of the upper half plane . The proof is bas…
Inequalities for geometric mean distance metric
Oona Rainio
We study a hyperbolic type metric introduced by Dovgoshey, Hariri, and Vuorinen. We find the best constant , for which this function is a metric in specifi…
Intrinsic metrics defined with arithmetic and logarithmic mean values
Oona Rainio, Rahim Kargar
We introduce several new functions that measure the distance between two points and in a domain by using the arithmetic or the logarithmic mean of…
Lipschitz constants and quadruple symmetrization by Möbius transformations
Oona Rainio, Matti Vuorinen
Due to the invariance properties of cross-ratio, Möbius transformations are often used to map a set of points or other geometric object into a symmetric position to simplify a prob…
Hilbert metric in the unit ball
Oona Rainio, Matti Vuorinen
The Hilbert metric between two points in a bounded convex domain is defined as the logarithm of the cross-ratio of and the intersection points of the Euclidean line…
Inequalities for the generalized point pair function
Oona Rainio
We study a new generalized version of the point pair function defined with a constant . We prove that this function is a quasi-metric for all values of , and compare it t…
Collinearity of points on Poincaré unit disk and Riemann sphere
Masayo Fujimura, Oona Rainio, Matti Vuorinen
We study certain points significant for the hyperbolic geometry of the unit disk. We give explicit formulas for the intersection points of the Euclidean lines and the stereographic…
Inclusion properties of the triangular ratio metric balls
Oona Rainio
Inclusion properties are studied for balls of the triangular ratio metric, the hyperbolic metric, the -metric, and the distance ratio metric defined in the unit ball domain. S…
Metrics and quasimetrics induced by point pair function
Dina Dautova, Semen Nasyrov, Oona Rainio +1
We study the point pair function in subdomains of . We prove that, for every domain , the this function is a quasi-metric with the consta…
Intrinsic metrics in ring domains
Oona Rainio
Three hyperbolic type metrics including the triangular ratio metric, the -metric and the Möbius metric are studied in an annular ring. The Euclidean midpoint rotation is intro…
Möbius metric in sector domains
Oona Rainio, Matti Vuorinen
The Möbius metric is studied in the cases where its domain is an open sector of the complex plane. We introduce upper and lower bounds for this metric in terms of the hyp…
Intrinsic metrics under conformal and quasiregular mappings
Oona Rainio
The distortion of six different intrinsic metrics and quasi-metrics under conformal and quasiregular mappings is studied in a few simple domains . The alre…
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…
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…