The fixed points of an analytic self-mapping
S. D. Fisher and John Franks
Proc. Amer. Math. Soc. 99 (1987), 76-78
Primary 30F10; Secondary 30C25, 55M20, 57M12
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Abstract: Let be a hyperbolic Riemann surface embedded in a compact Riemann surface of genus and let be an analytic function mapping into not the identity function. Then has as most distinct fixed points in ; equality may hold. If has 2 or more distinct fixed points, then is a periodic conformal automorphism of onto itself. This paper contains a proof of this theorem and several related results.
M. Farkas and Irwin
Kra, Riemann surfaces, Graduate Texts in Mathematics,
vol. 71, Springer-Verlag, New York-Berlin, 1980. MR 583745
Richards, and B.
Rodin, Analytic self-mappings of Riemann surfaces, J. Analyse
Math. 18 (1967), 197–225. MR 0212182
Maskit, The conformal group of a plane domain, Amer. J. Math.
90 (1968), 718–722. MR 0239078
- H. Farkas and I. Kra, Riemann surfaces, Graduate Texts in Math., vol. 71, Springer-Verlag, Berlin, 1980. MR 583745 (82c:30067)
- A. Marden, I. Richards and B. Rodin, Analytic self-mappings on Riemann surfaces, J. Analyse Math. 18 (1967), 197-226. MR 0212182 (35:3057)
- B. Maskit, The conformal group of a plane domain, Amer. J. Math. 90 (1968), 718-722. MR 0239078 (39:437)
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