Characterization of tangent quasicircles and quasiannuli
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914338835529728 |
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| author | Ntalampekos, Dimitrios |
| author_facet | Ntalampekos, Dimitrios |
| contents | We give a necessary and sufficient condition so that a pair of disjoint Jordan regions in the sphere can be quasiconformally mapped to a pair of disks. As a consequence, we obtain a simple characterization that involves Lipschitz functions for the case that one of the Jordan regions is a half-plane. We apply these results to prove that all polynomial cusps are quasiconformally equivalent and that a quasisymmetric embedding of the union of two disjoint disks extends to a quasiconformal map of the sphere, quantitatively. Also, in combination with previous work of the author, we obtain a new characterization of compact sets that are quasiconformally equivalent to Schottky sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17236 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterization of tangent quasicircles and quasiannuli Ntalampekos, Dimitrios Complex Variables Dynamical Systems Metric Geometry Primary 30C62, 30C20, Secondary 30F10, 30F45 We give a necessary and sufficient condition so that a pair of disjoint Jordan regions in the sphere can be quasiconformally mapped to a pair of disks. As a consequence, we obtain a simple characterization that involves Lipschitz functions for the case that one of the Jordan regions is a half-plane. We apply these results to prove that all polynomial cusps are quasiconformally equivalent and that a quasisymmetric embedding of the union of two disjoint disks extends to a quasiconformal map of the sphere, quantitatively. Also, in combination with previous work of the author, we obtain a new characterization of compact sets that are quasiconformally equivalent to Schottky sets. |
| title | Characterization of tangent quasicircles and quasiannuli |
| topic | Complex Variables Dynamical Systems Metric Geometry Primary 30C62, 30C20, Secondary 30F10, 30F45 |
| url | https://arxiv.org/abs/2602.17236 |