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Articles

Invariant metrics on the symmetrized bidisc

Pages 559-565 | Received 16 Mar 2014, Accepted 18 Jul 2014, Published online: 28 Aug 2014
 

Abstract

We find the explicit formulas of the Bergman and the Carathéodory metrics for the symmetrized bidisc . We also show that the Carathéodory metric for is not differentiable.

AMS Subject Classifications:

Acknowledgements

The author would like to thank Prof. Nikolai Nikolov and Prof. Włodzimierz Zwonek for help in preparation of the final version of the paper.

Additional information

Funding

The author is supported by international PhD programme “Geometry and Topology in Physical Models” of the Foundation for Polish Science. The paper was finished while she was a guest at the Institute of Mathematics and Informatics, Bulgarian Academy of Science October–December 2013.

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