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Lookup NU author(s): Professor Jim Agler, Dr Zinaida LykovaORCiD, Professor Nicholas Young
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND).
The symmetrized bidisc \[G \stackrel{\rm{def}}{=}\{(z+w,zw):|z|<1,\ |w|<1\}\]has interesting geometric properties. While it has a plentiful supply of complex geodesics and of automorphisms, there is nevertheless a unique complex geodesic $\mathcal{R}$ in $G$ that is invariant under all automorphisms of $G$. Moreover, $G$ is foliated by those complex geodesics that meet $\mathcal{R}$ in one point and have nontrivial stabilizer.We prove that these properties, together with two further geometric hypotheses on the action of the automorphism group of $G$, characterize the symmetrized bidisc in the class of complex manifolds.
Author(s): Agler J, Lykova ZA, Young NJ
Publication type: Article
Publication status: Published
Journal: Journal of Mathematical Analysis and Applications
Year: 2019
Volume: 473
Issue: 2
Pages: 1377-1413
Print publication date: 15/05/2019
Online publication date: 16/01/2019
Acceptance date: 09/01/2019
Date deposited: 10/01/2019
ISSN (print): 0022-247X
Publisher: Elsevier
URL: https://doi.org/10.1016/j.jmaa.2019.01.027
DOI: 10.1016/j.jmaa.2019.01.027
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