Blaschke product for bordered surfaces


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.

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

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Correspondence to A. B. Bogatyrev.

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To the memory of Sasha Vasil’ev.

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Supported by the Program of the Russ. Acad. Sci. ‘Fundamental Mathematics and its Applications’ under Grant PRAS-18-01.

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Bogatyrev, A.B. Blaschke product for bordered surfaces. Anal.Math.Phys. 9, 1877–1886 (2019).

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  • Ahlfors map
  • Schottky double
  • Riemann bilinear relations
  • Theta functions

Mathematics Subject Classification

  • 30F50
  • 30F30
  • 30C70