Schwarzian derivatives and a linearly invariant family in ℂⁿ

Rodrigo Hernández R.

Vol. 228 (2006), No. 2, 201–218

DOI: 10.2140/pjm.2006.228.201

Abstract

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 𝒮F. We use the Bergman metric to define a norm ∥𝒮F∥ 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.

Keywords

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

Mathematical Subject Classification 2000

Primary: 32A17, 32W50

Secondary: 32H02, 30C35

Milestones

Received: 7 March 2005

Revised: 4 September 2006

Accepted: 5 September 2006

Published: 1 December 2006