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.
KeywordsAhlfors map Schottky double Riemann bilinear relations Theta functions
Mathematics Subject Classification30F50 30F30 30C70
Funding was provided by RAS Program “Fundamental mathematics and its applications” (Grant No. PRAS-18-01).
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Conflict of interest
The author declares that he has no conflict of interest.
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