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Displaying similar documents to “The Schwarzian derivative for conformal maps.”

A topological dichotomy with applications to complex analysis

Iosif Pinelis (2015)

Colloquium Mathematicae

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Let X be a compact topological space, and let D be a subset of X. Let Y be a Hausdorff topological space. Let f be a continuous map of the closure of D to Y such that f(D) is open. Let E be any connected subset of the complement (to Y) of the image f(∂D) of the boundary ∂D of D. Then f(D) either contains E or is contained in the complement of E. Applications of this dichotomy principle are given, in particular for holomorphic maps, including maximum and minimum modulus...