# The Riemann mapping theorem for semianalytic domains and o-minimality

@article{Kaiser2009TheRM, title={The Riemann mapping theorem for semianalytic domains and o-minimality}, author={Tobias Kaiser}, journal={Proceedings of The London Mathematical Society}, year={2009}, volume={98}, pages={427-444} }

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 (i.e. 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… Expand

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