Conformal weldings in the Loewner equation and Weil--Petersson quasislit-disks
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| Format: | Preprint |
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2024
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| _version_ | 1866929550026342400 |
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| author | Tao, Fei Wei, Huaying Yang, Yaosong |
| author_facet | Tao, Fei Wei, Huaying Yang, Yaosong |
| contents | 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 $ϕ$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_14346 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal weldings in the Loewner equation and Weil--Petersson quasislit-disks Tao, Fei Wei, Huaying Yang, Yaosong Complex Variables Classical Analysis and ODEs 30C62, 30C75, 30H25 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 $ϕ$. |
| title | Conformal weldings in the Loewner equation and Weil--Petersson quasislit-disks |
| topic | Complex Variables Classical Analysis and ODEs 30C62, 30C75, 30H25 |
| url | https://arxiv.org/abs/2410.14346 |