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