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arXiv · 2410.14346

Conformal weldings in the Loewner equation and Weil--Petersson quasislit-disks

Fei Tao·Huaying Wei·Yaosong Yang
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Abstract

A simple arc $Γ= γ(0, T]$, growing into the unit disk $\mathbb D$ from its boundary, generates a driving term $ξ$ and a conformal welding $ϕ$ through the Loewner differential equation. When $Γ$ is the slit of a Weil--Petersson quasislit-disk $\mathbb D\setminusΓ$, the Loewner transform and its inverse $Γ\leftrightarrow ξ$ have been well understood due to Y. Wang's work. We investigate the maps $Γ\leftrightarrow ϕ$ in this case, giving a description of $Γ$ in terms of $ϕ$.

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Fei Tao, Huaying Wei, Yaosong Yang. 2024-10-18. Conformal weldings in the Loewner equation and Weil--Petersson quasislit-disks. https://arxiv.org/abs/2410.14346

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