Entire functions arising from trees

Weiwei Cui

Research output: Contribution to journalArticlepeer-review

Abstract

Given any infinite tree in the plane satisfying certain topological conditions, we construct an entire function f with only two critical values ±1 and no asymptotic values such that f−1([−1, 1]) is ambiently homeomorphic to the given tree. This can be viewed as a generalization of the result of Grothendieck (see Schneps (1994)) to the case of infinite trees. Moreover, a similar idea leads to a new proof of the result of Nevanlinna (1932) and Elfving (1934).

Original languageEnglish
Pages (from-to)2231-2248
JournalScience China Mathematics
Volume64
Issue number10
Early online date2021 Aug 11
DOIs
Publication statusPublished - 2021

Subject classification (UKÄ)

  • Discrete Mathematics

Free keywords

  • 30D15
  • 30D20
  • 30F20
  • entire function
  • Riemann surface
  • Shabat
  • the type problem
  • tree

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