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Lipschitz constants and quadruple symmetrization by Möbius transformations




TekijätRainio Oona, Vuorinen Matti

KustantajaSpringer International Publishing

Julkaisuvuosi2024

JournalComplex Analysis and its Synergies

Tietokannassa oleva lehden nimiComplex Analysis and its Synergies

Artikkelin numero8

Vuosikerta10

Numero2

eISSN2197-120X

DOIhttps://doi.org/10.1007/s40627-024-00136-y

Verkko-osoitehttps://doi.org/10.1007/s40627-024-00136-y

Rinnakkaistallenteen osoitehttps://research.utu.fi/converis/portal/detail/Publication/387700827


Tiivistelmä
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