The fixed points of an analytic self-mapping
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- by S. D. Fisher and John Franks PDF
- Proc. Amer. Math. Soc. 99 (1987), 76-78 Request permission
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.References
- Hershel M. Farkas and Irwin Kra, Riemann surfaces, Graduate Texts in Mathematics, vol. 71, Springer-Verlag, New York-Berlin, 1980. MR 583745
- A. Marden, I. Richards, and B. Rodin, Analytic self-mappings of Riemann surfaces, J. Analyse Math. 18 (1967), 197–225. MR 212182, DOI 10.1007/BF02798045
- Bernard Maskit, The conformal group of a plane domain, Amer. J. Math. 90 (1968), 718–722. MR 239078, DOI 10.2307/2373479
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 76-78
- MSC: Primary 30F10; Secondary 30C25, 55M20, 57M12
- DOI: https://doi.org/10.1090/S0002-9939-1987-0866433-8
- MathSciNet review: 866433