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arXiv · 1710.05952

On the harmonic M\"obius transformations

Rodrigo Hernández·María J. Martín
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Abstract

It is well-known that two locally univalent analytic functions $\varphi$ and $\psi$ have equal Schwarzian derivative if and only if there exists a non-constant M\"obius transformation $T$ such that $\varphi=T\circ \psi$. In this paper, we identify completely the relationship between two locally univalent harmonic mappings with equal (harmonic) Schwarzian derivative.

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Rodrigo Hernández, María J. Martín. 2017-10-16. On the harmonic M\"obius transformations. https://arxiv.org/abs/1710.05952

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