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The hyperbolic geometry of the symmetrized bidisc

Lookup NU author(s): Professor Jim Agler, Emeritus Professor Nicholas Young

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Abstract

We solve the Caratheodory and Kobayashi extremal problems for the open symmetrized bidisc G def= {(z1 + z2, z1 z 2) : |z1| < 1, |z2| < 1} ⊂ 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. G is the first example of a non convexifiable domain for which the two distances coincide.

Publication metadata

Author(s): Agler J, Young NJ

Publication type: Article

Publication status: Published

Journal: Journal of Geometric Analysis

Year: 2004

Volume: 14

Issue: 3

Pages: 375-403

Print publication date: 01/01/2004

ISSN (print): 1050-6926

ISSN (electronic): 1559-002X

Publisher: Springer

URL: http://dx.doi.org/10.1007/BF02922097

DOI: 10.1007/BF02922097

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