Abstract
Each holomorphic automorphism of an arbitrary domain G⊂S2, which has three distinct fixed points in G, reduces to the identity. This is known for domains of finite connectivity and is here proved in full generality by means of the Poincaré-metric of hyperbolic domains and some simple results of Riemannian Geometry.
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Literatur
GOLUZIN, G. M.: Geometric Theory of Functions of a Complex Variable, Translations of Mathematical Monographs (AMS), Vol. 26, Providence 1969
GROMOLL, D., KLINGENBERG, W., MEYER, W.: Riemannsche Geometrie im Großen, 2. Aufl., Springer Lecture Notes in Mathematics 55, Berlin-Heidelberg-New York: Springer 1975
PESCHL, E.: Über das Fixpunktverhalten von Automorphismen beliebiger Bereiche (erscheint demnächst)
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Leschinger, K. Über Fixpunkte holomorpher Automorphismen. Manuscripta Math 25, 391–396 (1978). https://doi.org/10.1007/BF01168050
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DOI: https://doi.org/10.1007/BF01168050