Abstract
Let G ⊆ C2 be the open symmetrized bidisc, namely G = {(λ1 + λ2, λ1λ2) : |λ1| < 1, |λ2| < 1}. In this paper, a proof is given that G is not biholomorphic to any convex domain in C2. By combining this result with earlier work of Agler and Young, the author shows that G is a bounded domain on which the Carathéodory distance and the Kobayashi distance coincide, but which is not biholomorphic to a convex set. 2000 Mathematics Subject Classification 32F45 (primary), 15A18 (secondary).
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