On the Harmonic Möbius Transformations

Rodrigo Hernández; María J. Martín

doi:10.1007/s12220-021-00809-8

On the Harmonic Möbius Transformations

Rodrigo Hernández, María J. Martín

Faculty of Engineering and Science

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

It is well-known that two locally univalent analytic functions have equal Schwarzian derivative if and only if each one of them is a composition of the other with a non-constant Möbius transformation. The main goal in this paper is to extend this result to the cases when the functions considered are harmonic. That is, we identify completely the transformations that preserve the (harmonic) Schwarzian derivative of locally univalent harmonic functions.

Original language	English
Article number	18
Journal	Journal of Geometric Analysis
Volume	32
Issue number	1
DOIs	https://doi.org/10.1007/s12220-021-00809-8
State	Published - Jan 2022

Keywords

Harmonic mappings
Möbius transformations
Schwarzian derivative

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10.1007/s12220-021-00809-8

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On the Harmonic Möbius Transformations

Abstract

Keywords

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