A Geometric Characterization of the Symmetrized Bidisc
| Autor: | Agler, Jim, Lykova, Zinaida, Young, N. J. |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Journal of Mathematical Analysis and Applications, 2019 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jmaa.2019.01.027 |
| Popis: | 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. Comment: 45 pages, 1 figure, with index. To appear in J. Math. Anal. Applic |
| Databáze: | arXiv |
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