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Seminar on Complex Analysis (Gonchar Seminar)
April 25, 2016 17:00, Moscow, Steklov Mathematical Institute, Room 411 (8 Gubkina)
 


Families of rational functions uniformizing Riemann surfaces over the sphere

S. R. Nasyrov

Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University

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Abstract: We deduce differential equation for a smooth one-parametric family of rational functions which maps the Riemann sphere onto a given family of ramified coverings of the sphere. As a corollary, we find a system of ODE for the critical points and the poles of these rational functions; the right-hand sides of the equations also depend on the corresponding critical values. The results are used in the problem of uniformization of given compact simply-connected Riemann surfaces over the sphere. The case of genus one (complex tori) is considered as well.

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