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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The fixed points of an analytic self-mapping


Authors: S. D. Fisher and John Franks
Journal: Proc. Amer. Math. Soc. 99 (1987), 76-78
MSC: Primary 30F10; Secondary 30C25, 55M20, 57M12
MathSciNet review: 866433
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Abstract: Let $ R$ be a hyperbolic Riemann surface embedded in a compact Riemann surface of genus $ g$ and let $ f$ be an analytic function mapping $ R$ into $ R, f$ not the identity function. Then $ f$ has as most $ 2g + 2$ distinct fixed points in $ R$; equality may hold. If $ f$ has 2 or more distinct fixed points, then $ f$ is a periodic conformal automorphism of $ R$ onto itself. This paper contains a proof of this theorem and several related results.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0866433-8
PII: S 0002-9939(1987)0866433-8
Article copyright: © Copyright 1987 American Mathematical Society