Univalence of holomorphic mappings

Molzon, Robert; Mortensen, Karen Pinney

doi:10.2140/pjm.1997.180.125

Cited by 5 publications

(2 citation statements)

References 9 publications

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“…[8]), although results relating it to the aforementioned problems of univalence and distortion are less satisfactory than in one variable. Consider the following overdetermined system of partial differential equations,…”

Section: Introductionmentioning

confidence: 95%

Schwarzian derivatives and some criteria for univalence in

Hernández

2007

Complex Variables and Elliptic Equations

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Oda gave a definition for Schwarzian derivatives in several complex variables [Oda, T., 1974, On Schwarzian derivatives in several variables (in Japanese). Kokyuroku Research Institute for Mathematical Sciences, Kioto University, 226, 82-85.], which we used in [Herna´ndez, R., Schwarzian derivatives and linear invariant families in C n . Journal of Mathematics (to appear).] to define a Schwarzian operator. In this article, we prove that different kinds of bounds on the norm of the Schwarzian operator imply univalence in the unit ball B n and on convex domains. We adapt Sturm comparison techniques to study the zero sets of a set of linearly independent solutions to a system of differential equations associated with the Schwarzian derivatives.

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Section: Introductionmentioning

confidence: 95%

Schwarzian derivatives and some criteria for univalence in

Hernández

2007

Complex Variables and Elliptic Equations

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“…But for n > 1 the number of parameters involved in the value and all derivatives of order 1 and 2 of a locally biholomorphic mapping is n A different approach to obtain the invariant operators S k ij , S 0 ij has been developed by Molzon and Tamanoi [14]. In addition, Molzon and Pinney had earlier developed equivalent invariant operators in the context of complex manifolds [13].…”

Section: Introductionmentioning

confidence: 99%