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 language | English |
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Pages (from-to) | 2231-2248 |
Journal | Science China Mathematics |
Volume | 64 |
Issue number | 10 |
Early online date | 2021 Aug 11 |
DOIs | |
Publication status | Published - 2021 |
Subject classification (UKÄ)
- Discrete Mathematics
Free keywords
- 30D15
- 30D20
- 30F20
- entire function
- Riemann surface
- Shabat
- the type problem
- tree