Abstract
Modifying the classical theorems of Schottky and Landau, the author obtains the converses of these theorems. More precisely, the author defines the notions of Schottky, Landau and Picard properties and proves that a plane domain D D satisfies any of these properties if and only if C ∖ D {\mathbf {C}}\backslash D contains at least two points. The method of proofs is completely elementary and uses only some basic properties of the Kobayashi metric.
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