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}
}
  • Tobias Kaiser
  • Published 2009
  • Mathematics
  • Proceedings of The London Mathematical Society
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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