Value Ranges of Univalent Self-Mappings of the Unit Disc

2015/08/19 by Koch, Julia, Schleissinger, Sebastian
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1508.04659

Abstract

We describe the value set \f(z₀) : f:\mathbbD→\mathbbD univalent, f(0)=0, f'(0)= e^-T \, where \mathbbD denotes the unit disc and z₀∈\mathbbD∖\0\, T>0, by applying Pontryagin's maximum principle to the radial Loewner equation.

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