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arXiv · 1508.04659

Value Ranges of Univalent Self-Mappings of the Unit Disc

Julia Koch·Sebastian Schleissinger
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Abstract

We describe the value set $\{f(z_0)\,:\, f:\mathbb{D}\to\mathbb{D} \text{ univalent}, f(0)=0, f'(0)= e^{-T} \},$ where $\mathbb{D}$ denotes the unit disc and $z_0\in\mathbb{D}\setminus\{0\}$, $T>0,$ by applying Pontryagin's maximum principle to the radial Loewner equation.

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Julia Koch, Sebastian Schleissinger. 2015-09-17. Value Ranges of Univalent Self-Mappings of the Unit Disc. https://arxiv.org/abs/1508.04659

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