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Towards an Effectivisation of the Riemann Theorem

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Abstract

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 ℂ. 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.

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Authors and Affiliations

  1. Institute for Theoretical and Experimental Physics, Moscow State University, Independent University of Moscow, Moscow, Russia

    S. Natanzon

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  1. S. Natanzon
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Correspondence to S. Natanzon.

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Communicated by M. A. Shubin (Moscow)

Mathematics Subject Classifications (2000): 30Cxx, 37Kxx.

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Natanzon, S. Towards an Effectivisation of the Riemann Theorem. Ann Glob Anal Geom 28, 233–255 (2005). https://doi.org/10.1007/s10455-005-7276-5

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  • DOI: https://doi.org/10.1007/s10455-005-7276-5

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