Prescribing the preSchwarzian in several complex variables

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We solve the several complex variables preSchwarzian operator equation [Df(z)]-1 D2f(z) = A(z), z € Cn, where A(z) is a bilinear operator and f is a Cn valued locally biholomorphic function on a domain in Cn. Then one can define a several variables f → fα transform via the operator equation [Dfα(z)]-1D2fα(z) = a[Df(z)]-1D2f(z), and thereby, study properties of fα. This is a natural generalization of the one variable operator fα(z) in [6] and the study of its univalence properties, e.g., the work of Royster [23] and many others. Möbius invariance and the multivariables Schwarzian derivative operator of Oda [17] play a central role in this work.

Original languageEnglish
Pages (from-to)331-340
Number of pages10
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Issue number1
StatePublished - 2011


  • Holomorphic mapping
  • PreSchwarzian derivative
  • Univalence


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