A Geometric Characterization of the Symmetrized Bidisc

10 Jan 2019 Agler Jim Lykova Zinaida Young N. J.

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 $G$... (read more)

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