The hyperbolic geometry of the symmetrized bidisc

Jim Agler and Nicholas Young

Keywords

mu-synthesis, interpolation,Caratheodory distance, Kobayashi distance

Status

Appeared in the Journal of Geometric Analysis, volume 14, pages 375-403, 2004.

Abstract

We solve the Caratheodory and Kobayashi extremal problems for the open symmetrized bidisc

G = {(z+w, zw): |z| < 1, |w| < 1}, a domain in C^2.

We prove the equality of the Caratheodory and Kobayashi distances on G and describe the extremal functions for the two problems; they are rational of degree 1 or 2.

J. Agler's work is suported by an NSF grant in Modern Analysis. This work was also supported by an EPSRC Visiting Fellowship.

The preprint is available as a dvi file.

Nicholas Young
7th September, 2003; revised 14th May 2004
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