Annals of Global Analysis and Geometry

, Volume 28, Issue 3, pp 233–255 | Cite as

Towards an Effectivisation of the Riemann Theorem

  • S. NatanzonEmail author


Let Q be a connected and simply connected domain on the Riemann sphere, not coinciding with the Riemann sphere and with the whole complex plane . Then, according to the Riemann Theorem, there exists a conformal bijection between Q and the exterior of the unit disk. In this paper, we find an explicit form of this map for a broad class of domains with analytic boundaries.


Riemann theorem Toda hierarchy 


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© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Institute for Theoretical and Experimental Physics, Moscow State UniversityIndependent University of MoscowMoscowRussia

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