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.

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.

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.