Geodesics, Retracts, and the Norm-Preserving Extension Property in the Symmetrized Bidisc

Jim Agler, University of California at San Diego, CA.Zinaida Lykova, Newcastle University, Newcastle upon Tyne, United Kingdom.Nicholas Young, Newcastle University, Newcastle upon Tyne, United Kingdom.

• IntroductionAn overviewExtremal problems in the symmetrized bidisc $G$Complex geodesics in $G$The retracts of $G$ and the bidisc $\mathbb {D}^2$Purely unbalanced and exceptional datums in $G$A geometric classification of geodesics in $G$Balanced geodesics in $G$Geodesics and sets $V$ with the norm-preserving extension property in $G$Anomalous sets $\mathcal {R}\cup \mathcal {D}$ with the norm-preserving extension property in $G$$V$ and a circular region $R$ in the planeProof of the main theoremSets in $\mathbb {D}^2$ with the symmetric extension propertyApplications to the theory of spectral setsAnomalous sets with the norm-preserving extension property in some other domainsAppendix A. Some useful facts about the symmetrized bidiscAppendix B. Types of geodesic: a crib and some cartoonsBibliographyIndex.