Inequalities for a new hyperbolic type metric

: Rainio, Oona

Publisher: Springer Science and Business Media LLC

: 2025

: Complex Analysis and its Synergies

: 3

: 11

: 2

: 2524-7581

: 2197-120X

DOI: https://doi.org/10.1007/s40627-025-00151-7

: https://doi.org/10.1007/s40627-025-00151-7

: https://research.utu.fi/converis/portal/detail/Publication/491703735

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 inequalities with the hyperbolic metric and the triangular ratio metric. We also improve existing ball inclusion results and give bounds for the distortion of this new metric under conformal and quasiregular mappings.

s40627-025-00151-7.pdf

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Open Access funding provided by University of Turku (including Turku University Central Hospital). My research was funded by Magnus Ehrnrooth Foundation and the Finnish Cultural Foundation.