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Numerical Schottky Uniformizations: Myrberg’s Opening Process

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Computational Approach to Riemann Surfaces

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2013))

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Abstract

It is well known that a closed Riemann surface may be described by different king of objects; for instance, by algebraic curves, Fuchsian groups, Schottky groups, Riemann period matrices, ext. In general, if one knows explicitly one of these presentations, it is a very hard problem to provide the others in an explicit way. In the 1920s, Myrberg [Myr16] proposed an algorithm which permits to approximate numerically a Schottky uniformization of a hyperelliptic Riemann surface once an explicit hyperelliptic curve presentation is given.

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Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Técnica Federico Santa María, Valparaíso, Chile

    Rubén A. Hidalgo

  2. Department of Mathematics, Florida State University, Tallahassee, USA

    Mika Seppälä

  3. Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland

    Mika Seppälä

Authors
  1. Rubén A. Hidalgo
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  2. Mika Seppälä
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Corresponding author

Correspondence to Rubén A. Hidalgo .

Editor information

Editors and Affiliations

  1. Institute of Mathematics, Technical University of Berlin, Straße des 17.Juni 136, Berlin, 10623, Germany

    Alexander I. Bobenko

  2. Institut de Mathématiques, Université de Bourgogne, av. Alain Savary 9, Dijon Cedex, 21078, France

    Christian Klein

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Hidalgo, R.A., Seppälä, M. (2011). Numerical Schottky Uniformizations: Myrberg’s Opening Process. In: Bobenko, A., Klein, C. (eds) Computational Approach to Riemann Surfaces. Lecture Notes in Mathematics(), vol 2013. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17413-1_6

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