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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The Kobayashi indicatrix at the center of a circular domain


Author: Theodore J. Barth
Journal: Proc. Amer. Math. Soc. 88 (1983), 527-530
MSC: Primary 32F15; Secondary 32A07, 32H15
DOI: https://doi.org/10.1090/S0002-9939-1983-0699426-0
MathSciNet review: 699426
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Abstract: The indicatrix of the Kobayashi infinitesimal metric at the center of a pseudoconvex complete circular domain coincides with this domain. It follows that a nonconvex complete circular domain cannot be biholomorphic to any convex domain. An example shows that a bounded pseudoconvex complete circular domain in $ {{\mathbf{C}}^2}$ need not be taut.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0699426-0
Keywords: Kobayashi metric, complete circular domain, taut domain, pseudoconvex domain, convex domain
Article copyright: © Copyright 1983 American Mathematical Society