Schwarzian derivatives and a linearly invariant family in ℂn

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We use Oda's definition of the Schwarzian derivative for locally univalent holomorphic maps F in several complex variables to define a Schwarzian derivative operator ΦF. We use the Bergman metric to define a norm ||φF|| for this operator, which in the ball is invariant under composition with automorphisms. We study the linearly invariant family estimating its order and norm order.

Original languageEnglish
Pages (from-to)201-218
Number of pages18
JournalPacific Journal of Mathematics
Issue number2
StatePublished - 2006


  • Linearly invariant families
  • Schwarzian derivative
  • Several complex varaibles
  • Sturm comparison


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