33 citations · 140 across the 29 of their papers we have counts for
6 papers · 1 filter
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…
Uniformly perfect sets, Hausdorff dimension, and conformal capacity
Oona Rainio, Toshiyuki Sugawa, Matti Vuorinen
Using the definition of uniformly perfect sets in terms of convergent sequences, we apply lower bounds for the Hausdorff content of a uniformly perfect subset of …
Conformally invariant metrics and lack of Hölder continuity
Rahim Kargar, Oona Rainio
The modulus metric between two points in a subdomain of is defined in terms of moduli of curve families joining the boundary of the domain with a continuum…
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…