Abstract
The Koebe domain of a family of functions, holomorphic on the unit disk, is the largest domain that is contained in the image of the unit disk for every function of the family. In this note, we furnish a geometric proof of a classical theorem due to Landau on the Koebe domains for certain families of holomorphic functions. The method of proof involves our recently obtained results concerning estimates for hyperbolic metrics on subdomains.
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