The complex geodesics of the symmetrized bidisc

Jim Agler and Nicholas Young

Keywords

mu-synthesis, interpolation, Caratheodory distance, Kobayashi distance

Status

To appear in International J. Math.

Abstract

We give formulae for all complex geodesics of the symmetrised bidisc $G$. There are two classes of geodesics: flat ones, indexed by the unit disc, and geodesics of degree $2$, naturally indexed by $G$ itself. The flat geodesics foliate $G$, and there is a unique geodesic through every pair of points of $G$. We also obtain a trichotomy result for left inverses of complex geodesics.

J. Agler's work is suported by an NSF grant in Modern Analysis. This work was also supported by the UK Engineering and Physical Sciences Research Council grant GR/T20014/01.

The preprint is available as a pdf file.

Nicholas Young
6th June, 2005.