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Seminar on Complex Analysis (Gonchar Seminar)
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Blaschke product for bordered surface A. B. Bogatyrev Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow |
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Abstract: It is well known that a ramified holomorphic covering of a closed unitary disc by another such a disc is given by a finite Blaschke product. The inverse is also true. We give an explicit description of holomorphic ramified coverings of a disc by another bordered Riemann surface. The problem of covering a disc by an annulus arises e.g. in multidimensional complex analysis; we show that it may be effectively solved in terms of elliptic theta functions. The covering of a disc by a multiconnected flat domain was discussed in G.M.Golusin's book. |