On the Harmonic Möbius Transformations

Rodrigo Hernández, María J. Martín

Research output: Contribution to journalArticlepeer-review

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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 languageEnglish
Article number18
JournalJournal of Geometric Analysis
Issue number1
StatePublished - Jan 2022


  • Harmonic mappings
  • Möbius transformations
  • Schwarzian derivative


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