Inequalities for geometric mean distance metric

Oona Rainio

Inequalities for geometric mean distance metric

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arxiv 2404.01017 v1 pith:TY7BEU7H submitted 2024-04-01 math.MG

Oona Rainio This is my paper · ORCID

classification math.MG

keywords metrichyperbolicinequalitiestypeballbestchoicesconstant

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abstract

We study a hyperbolic type metric $h_{G,c}$ introduced by Dovgoshey, Hariri, and Vuorinen. We find the best constant $c>0$, for which this function $h_{G,c}$ is a metric in specific choices of $G$. We give several sharp inequalities between $h_{G,c}$ and other hyperbolic type metrics, and also offer a few results related to ball inclusion.

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On distortion of quasiregular mappings of the upper half plane
math.CV 2024-11 conditional novelty 7.0 of 10

For K-quasiregular maps of the upper half plane, the geometric-mean distance h_{H2,c} is shown to satisfy an explicit distortion bound, and h_{H2,c} is a metric for every c >= 1.

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