On Picard’s theorem for entire quasiregular mappings

Vuorinen, Matti

doi:10.1090/S0002-9939-1989-0975662-6

On Picard’s theorem for entire quasiregular mappings
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Proc. Amer. Math. Soc. 107 (1989), 383-394 Request permission

Abstract:

Several refinements of Picard’s theorem for entire functions in the complex plane have been proved by many authors in connection with the theory of Picard sets. We prove a result of this type for entire quasiregular mappings in euclidean $n$-space in the case when the "Picard set" consists of a sequence ${a_k}$ on a ray emanating from 0 with $|{a_k}| = {2^k}$.

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