Computational Methods and Function Theory 9 (2009), No. 2, 443--454
Copyright Heldermann Verlag 2009
Martin Chuaqui
mchuaqui@mat.puc.cl , Pontificia Universidad Católica de Chile, Facultad de Matemáticas, Casilla 306, Santiago 22, Chile.
Rodrigo Hernández
rodrigo.hernandez@uai.cl , Universidad Adolfo Ibánez, Facultad de Ciencias y Tecnología, Av. Diagonal las Torres 2640, Penalolen, Chile.
We study a sufficient condition for univalence in the polydisk in terms of the size of the norm of the Schwarzian operator. Examples show that our result is close to optimal in dimension two. This paper extends work by the second author concerning similar criteria in the ball.
Keywords: Schwarzian operator, univalence condition, polydisk, Bergman metric.
MSC 2000: Primary 32H02, 32A17; Secondary 30C45.
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