The Hayman--Wu constant is $\pi^2$

Paata Ivanisvili

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arXiv · 2608.12844

The Hayman--Wu constant is $\pi^2$

Paata Ivanisvili

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Abstract

We show that for every conformal map $\phi:\mathbb{D}\to\Omega\subsetneq\mathbb{C}$ from the unit disk onto a simply connected proper domain $\Omega$, the length of $\phi^{-1}(\Omega\cap L)$ is at most $\pi^2$ for every line $L$.

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Paata Ivanisvili. 2026-08-13. The Hayman--Wu constant is $\pi^2$. https://arxiv.org/abs/2608.12844

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