Uniformization of Simply-Connected Ramified Coverings of the Sphere by Rational Functions
- 10 Downloads
We deduce a systemofODEs describing behavior of critical points and poles of a smooth one-parametric family of rational functions uniformizing a given family of ramified coverings of the Riemann sphere.
Keywords and phrasesRiemann surface ramified covering rational function uniformization conformal mapping one-parametric family
Unable to display preview. Download preview PDF.
- 6.A. D. Mednykh, “Nonequivalent coverings of Riemann surfaces with a given branch type,” Sib. Math. J. 25 (4), 120–142 (1984).Google Scholar
- 7.S. R. Nasyrov, Geometric Problems of the Theory of Ramified Covetrings of Riemann Surfaces (Magarif, Kazan, 2008) [in Russian].Google Scholar
- 11.I. A. Alexandrov, Parametric Continuations in the Theory of Univalent Functions (Nauka, Moscow, 1976) [in Russian].Google Scholar