2023/08/12 by Oona Rainio, Rainio, Oona, Rahim Kargar +1
Mathematics · #Analytic and geometric function theory
paper · pdf · doi:10.48550/arxiv.2308.06576
We introduce several new functions that measure the distance between two points x and y in a domain G\subsetneqℝn by using the arithmetic or the logarithmic mean of the Euclidean distances from the points x and y to the boundary of G. We study in which domains these functions are metrics and find sharp inequalities between them and the hyperbolic metric. We also present one result about their distortion under quasiregular mappings.