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DESCRIPTION OF ALL COMPLEX GEODESICS IN THE SYMMETRIZED BIDISC
PETER PFLUG, WŁODZIMIERZ ZWONEK
Journal:

Bulletin of the London Mathematical Society / Volume 37 / Issue 4 / August 2005

Published online by Cambridge University Press:

02 August 2005, pp. 575-584

Print publication:

August 2005
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Effective formulae are found for the complex geodesics in the symmetrized bidisc.

THE SYMMETRIZED BIDISC AND LEMPERT'S THEOREM
C. COSTARA
Journal:

Bulletin of the London Mathematical Society / Volume 36 / Issue 5 / September 2004

Published online by Cambridge University Press:

24 August 2004, pp. 656-662

Print publication:

September 2004
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Let $G\subseteq \mathbb{C}^{2}$ be the open symmetrized bidisc, namely $G= \{(\lambda_{1}+\lambda_{2},\lambda_{1}\lambda_{2}):|\lambda_{1}|<1,|\lambda_{2}|<1\}$. In this paper, a proof is given that $G$ is not biholomorphic to any convex domain in $\mathbb{C}^{2}$. 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.