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

Introduction
An overview
Extremal 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 plane
Proof of the main theorem
Sets in $\mathbb {D}^2$ with the symmetric extension property
Applications to the theory of spectral sets
Anomalous sets with the norm-preserving extension property in some other domains
Appendix A. Some useful facts about the symmetrized bidisc
Appendix B. Types of geodesic: a crib and some cartoons
Bibliography
Index.