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Entire functions arising from trees

Cui, Weiwei LU (2021) In Science China Mathematics 64(10). p.2231-2248
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).

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
30D15, 30D20, 30F20, entire function, Riemann surface, Shabat, the type problem, tree
in
Science China Mathematics
volume
64
issue
10
pages
2231 - 2248
publisher
Science in China Press
external identifiers
  • scopus:85112199369
ISSN
1674-7283
DOI
10.1007/s11425-019-1644-0
language
English
LU publication?
yes
id
17a929ee-0ba4-4c1a-8d9f-ff2c7d3b4bcf
date added to LUP
2021-09-10 15:22:23
date last changed
2022-04-27 03:53:19
@article{17a929ee-0ba4-4c1a-8d9f-ff2c7d3b4bcf,
  abstract     = {{<p>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<sup>−1</sup>([−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).</p>}},
  author       = {{Cui, Weiwei}},
  issn         = {{1674-7283}},
  keywords     = {{30D15; 30D20; 30F20; entire function; Riemann surface; Shabat; the type problem; tree}},
  language     = {{eng}},
  month        = {{08}},
  number       = {{10}},
  pages        = {{2231--2248}},
  publisher    = {{Science in China Press}},
  series       = {{Science China Mathematics}},
  title        = {{Entire functions arising from trees}},
  url          = {{http://dx.doi.org/10.1007/s11425-019-1644-0}},
  doi          = {{10.1007/s11425-019-1644-0}},
  volume       = {{64}},
  year         = {{2021}},
}