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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.08485 |
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| _version_ | 1866909574366232576 |
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| author | Esmayli, Behnam Rajala, Kai |
| author_facet | Esmayli, Behnam Rajala, Kai |
| contents | We prove Koebe's conjecture and a version of Schramm's cofat uniformization theorem for domains $Ω\subset \mathbb C$ satisfying conditions involving quasitripods, i.e., quasisymmetric images of the standard tripod. If the non-point complementary components of $Ω$ contain uniform quasitripods with large diameters and satisfy a packing condition, then there exists a conformal map $f\colonΩ\to D$ onto a circle domain $D$. Moreover, $f$ preserves the classes of point-components and non-point components. The packing condition is satisfied if $Ω$ is cospread, i.e., if the complementary components contain uniform quasitripods in all scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08485 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal Uniformization of Domains Bounded by Quasitripods Esmayli, Behnam Rajala, Kai Complex Variables We prove Koebe's conjecture and a version of Schramm's cofat uniformization theorem for domains $Ω\subset \mathbb C$ satisfying conditions involving quasitripods, i.e., quasisymmetric images of the standard tripod. If the non-point complementary components of $Ω$ contain uniform quasitripods with large diameters and satisfy a packing condition, then there exists a conformal map $f\colonΩ\to D$ onto a circle domain $D$. Moreover, $f$ preserves the classes of point-components and non-point components. The packing condition is satisfied if $Ω$ is cospread, i.e., if the complementary components contain uniform quasitripods in all scales. |
| title | Conformal Uniformization of Domains Bounded by Quasitripods |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2401.08485 |