Mathematics – Logic
Scientific paper
2007-05-14
Mathematics
Logic
22 pages
Scientific paper
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 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 $\pi$.
No associations
LandOfFree
The Riemann Mapping Theorem for semianalytic domains and o-minimality does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Riemann Mapping Theorem for semianalytic domains and o-minimality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Riemann Mapping Theorem for semianalytic domains and o-minimality will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-365216