Abstract: This paper considers the number of discrete fixed points that an automorphism (biholomorphic self-map) of a complex domain or manifold can have. Our results give a geometric formulation to the problem and its solution; they generalize classical theorems in one complex variable.
IntroductionIt is a result of classical function theory (see [PEL], [SUI], [FIF], [MAS], [LES]) that if f : U → U is a conformal self-mapping of a plane domain which fixes three distinct points then f (ζ) ≡ ζ. The purpose of …
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