Kaiser, Tobias (2009) The Riemann mapping theorem for semianalytic domains and o-minimality. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 98. pp. 427-444. ISSN 0024-6115,
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We consider the Riemann mapping theorem in the case of a bounded simply connected and semianalytic domain. We show that the germ at 0 of the Riemann map (that is, biholomorphic map) from the upper half plane to such a domain can be realized in a certain quasianalytic class if the angle of the boundary at the point to which 0 is mapped is greater than 0. This quasianalytic class was introduced and used by Ilyashenko in his work on Hilbert's 16th problem. With this result, we can prove that the Riemann map from a bounded simply connected semianalytic domain onto the unit ball is definable in an o-minimal structure, provided that at singular boundary points the angles of the boundary are irrational multiples of pi.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | EXPONENTIAL FUNCTION; SUBANALYTIC SETS; REAL FIELD; EXPANSIONS; SERIES; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Professoren und akademische Räte im Ruhestand > Prof. Dr. Manfred Knebusch |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 Oct 2020 08:17 |
| Last Modified: | 05 Oct 2020 08:17 |
| URI: | https://pred.uni-regensburg.de/id/eprint/29438 |
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