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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 discand $z_0\in\mathbb{D}\setminus\{0\}$, $T>0,$ by applying Pontryagin's maximumprinciple to the radial Loewner equation.

Value Ranges of Univalent Self-Mappings of the Unit Disc