Characterization of John domains via weak tangents
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917284550803456 |
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| author | Karafyllia, Christina |
| author_facet | Karafyllia, Christina |
| contents | We characterize simply connected John domains in the plane with the aid of weak tangents of the boundary. Specifically, we prove that a bounded simply connected domain $D$ is a John domain if and only if, for every weak tangent $Y$ of $\partial D$, every connected component of the complement of $Y$ that ``originates" from $D$ is a John domain, not necessarily with uniform constants. Our main theorem improves a result of Kinneberg (arXiv:1507.04698), who obtains a necessary condition for a John domain in terms of weak tangents but not a sufficient one. We also establish several properties of weak tangents of John domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18425 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of John domains via weak tangents Karafyllia, Christina Complex Variables Metric Geometry Primary 30C20, 30C62, Secondary 30L10 We characterize simply connected John domains in the plane with the aid of weak tangents of the boundary. Specifically, we prove that a bounded simply connected domain $D$ is a John domain if and only if, for every weak tangent $Y$ of $\partial D$, every connected component of the complement of $Y$ that ``originates" from $D$ is a John domain, not necessarily with uniform constants. Our main theorem improves a result of Kinneberg (arXiv:1507.04698), who obtains a necessary condition for a John domain in terms of weak tangents but not a sufficient one. We also establish several properties of weak tangents of John domains. |
| title | Characterization of John domains via weak tangents |
| topic | Complex Variables Metric Geometry Primary 30C20, 30C62, Secondary 30L10 |
| url | https://arxiv.org/abs/2501.18425 |