Fixed points of analytic self-mappings of Riemann surfaces |
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Authors: | C. David Minda |
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Affiliation: | (1) Department of Mathematical Sciences, University of Cincinnati, 45221 Cincinnati, Ohio, USA |
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Abstract: | The existence of fixed points for an analytic self-mapping of a Riemann surface often permits strong conclusions about the mapping. For hyperbolic Riemann surfaces fixed point conditions that imply an analytic self-mapping is actually a conformal automorphism are given. For instance, an analytic self-mapping of a hyperbolic Riemann surface with two fixed points must be a conformal automorphism of finite order. On the other hand, for surfaces of finite genus estimates of the order of a conformal automorphism are obtained from fixed point information. For example, on a Riemann surface of genus g a conformal automorphism with 2g+3 fixed points is the identity. |
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