The Schwarzian Derivative for Convex Holomorphic Mappings in Several Complex Variables

Rodrigo Hernández

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arXiv · 2604.12010

The Schwarzian Derivative for Convex Holomorphic Mappings in Several Complex Variables

Rodrigo Hernández

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Abstract

We obtain upper bounds for the norm of the Schwarzian derivative of convex holomorphic mappings defined on the polydisk and the unit ball in $\mathbb{C}^n$. For coordinate-wise convex mappings on the polydisk, we derive a sharp estimate extending the classical one-variable result of Chuaqui--Duren--Osgood to higher dimensions. For the Roper--Suffridge extension operator in the unit ball, we obtain an explicit bound that represents the best available estimate in this setting.

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Rodrigo Hernández. 2026-04-13. The Schwarzian Derivative for Convex Holomorphic Mappings in Several Complex Variables. https://arxiv.org/abs/2604.12010

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