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Sharp radius for univalent convex functions

Context Koebe 1/4 Theorem states the following: Theorem.- Let $f \in \mathcal{S}$, that is, the set of univalent (analytic and injective) with $f(0)=0$ and $f’(0)=1$ functions from $\mathbb{D}=\lbrace z \in \mathbb{C}: \vert z \vert < 1 \rbrace$ to $\mathbb{C}$, then $D(0,1/4)=\lbrace z \in \mathbb{C}: \vert z \vert < 1/4 \rbrace \subset f(\mathbb{D})$. Furthermore, if there […]