Entire functions arising from trees
(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:
https://lup.lub.lu.se/record/17a929ee-0ba4-4c1a-8d9f-ff2c7d3b4bcf
- author
- Cui, Weiwei LU
- organization
- publishing date
- 2021-08-11
- 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}}, }