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- W2079561330 abstract "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 π." @default.
- W2079561330 created "2016-06-24" @default.
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- W2079561330 date "2008-08-22" @default.
- W2079561330 modified "2023-09-25" @default.
- W2079561330 title "The Riemann mapping theorem for semianalytic domains and o -minimality" @default.
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- W2079561330 doi "https://doi.org/10.1112/plms/pdn034" @default.
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