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Bounded type Siegel disks of finite type maps with few singular values
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Cheritat, Arnaud and Epstein, Adam L. (2018) Bounded type Siegel disks of finite type maps with few singular values. Science China Mathematics, 61 (12). pp. 2139-2156. doi:10.1007/s11425-018-9381-4
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WRAP-bounded-type-siegel-disks-finite-maps-values-Epstein-2018.pdf - Accepted Version - Requires a PDF viewer. Download (830Kb) | Preview |
Official URL: https://doi.org/10.1007/s11425-018-9381-4
Abstract
Let U be an open subset of the Riemann sphere C^ . We give sufficient conditions for which a finite type map f: U → C^ with at most three singular values has a Siegel disk compactly contained in U and whose boundary is a quasicircle containing a unique critical point. The main tool is quasiconformal surgery à la Douady-Ghys-Herman-Świątek. We also give sufficient conditions for which, instead, Δ has not compact closure in U. The main tool is the Schwarzian derivative and area inequalities à la Graczyk-Świątek.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Mappings (Mathematics), Riemann surfaces | ||||||||
| Journal or Publication Title: | Science China Mathematics | ||||||||
| Publisher: | Zhongguo Kexue Zazhishe | ||||||||
| ISSN: | 1674-7283 | ||||||||
| Official Date: | December 2018 | ||||||||
| Dates: |
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| Volume: | 61 | ||||||||
| Number: | 12 | ||||||||
| Page Range: | pp. 2139-2156 | ||||||||
| DOI: | 10.1007/s11425-018-9381-4 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | This is a post-peer-review, pre-copyedit version of an article published in Science China Mathematics. The final authenticated version is available online at: https://doi.org/10.1007/s11425-018-9381-4 | ||||||||
| Access rights to Published version: | Open Access | ||||||||
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