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Blaschke product for bordered surfaces

  • A. B. BogatyrevEmail author
Article

Abstract

Any ramified holomorphic covering of a closed unit disc by another such a disc is given by a finite Blaschke product. The inverse is also true. In this note we give two explicit constructions for a holomorphic ramified covering of a disc by other bordered Riemann surface. The machinery used here strongly resembles the description of magnetic configurations in submicron planar magnets.

Keywords

Ahlfors map Schottky double Riemann bilinear relations Theta functions 

Mathematics Subject Classification

30F50 30F30 30C70 

Notes

Acknowledgements

Funding was provided by RAS Program “Fundamental mathematics and its applications” (Grant No. PRAS-18-01).

Compliance with ethical standards

Conflict of interest

The author declares that he has no conflict of interest.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Marchuk Institute for Numerical MathematicsRussian Academy of SciencesMoscowRussia

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