A1 Refereed original research article in a scientific journal

Lipschitz constants and quadruple symmetrization by Möbius transformations



Authors: Rainio Oona, Vuorinen Matti

Publisher: Springer International Publishing

Publication year: 2024

Journal: Complex Analysis and its Synergies

Journal name in source: Complex Analysis and its Synergies

Article number: 8

Volume: 10

Issue: 2

eISSN: 2197-120X

DOI: https://doi.org/10.1007/s40627-024-00136-y

Web address : https://doi.org/10.1007/s40627-024-00136-y

Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/387700827


Abstract
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 problem studied. However, when the points are mapped under a Möbius transformation, the distortion of the Euclidean geometry is rarely considered. Here, we identify several cases where the distortion caused by this symmetrization can be measured in terms of the Lipschitz constant of the Möbius transformation in the Euclidean or the chordal metric.

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Last updated on 2024-26-11 at 21:27