The fixed points of an analytic self-mapping

S. D. Fisher, John Franks

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 conformai automorphism of R onto itself. This paper contains a proof of this theorem and several related results.

Original languageEnglish (US)
Pages (from-to)76-78
Number of pages3
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - Jan 1987

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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