Families of meromorphic functions avoiding continuous functions

D. Bargmann, M. Bonk, A. Hinkkanen, G. J. Martin

Research output: Contribution to journalArticlepeer-review


Let h1, h2 and h3 be continuous functions from the unit disk double-struck D sign into the Riemann sphere ℂ such that hi(z) ≠ hj(z) (i ≠ j) for each z ∈ double-struck D sign. We prove that the set ℱ of all functions f meromorphic on double-struck D sign such that f(z) ≠ hj(z) for all z ∈ D and j = 1, 2, 3 is a normal family. The result and the method of the proof extend to quasimeromorphic functions in higher dimensions as well.

Original languageEnglish (US)
Pages (from-to)379-387
Number of pages9
JournalJournal d'Analyse Mathematique
StatePublished - 1999

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)


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