Upper bounds for the Schwarzian derivative norm of convex holomorphic mappings are derived for the polydisk and unit ball in C^n, with a sharp estimate for coordinate-wise convex maps extending the one-variable Chuaqui-Duren-Osgood result and an explicit bound for Roper-Suffridge extensions.
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The Schwarzian Derivative for Convex Holomorphic Mappings in Several Complex Variables
Upper bounds for the Schwarzian derivative norm of convex holomorphic mappings are derived for the polydisk and unit ball in C^n, with a sharp estimate for coordinate-wise convex maps extending the one-variable Chuaqui-Duren-Osgood result and an explicit bound for Roper-Suffridge extensions.