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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The limiting behavior of the Kobayashi-Royden pseudometric


Author: Shulim Kaliman
Journal: Trans. Amer. Math. Soc. 339 (1993), 361-371
MSC: Primary 32H15; Secondary 30F45, 32E10, 32G10
MathSciNet review: 1118826
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Abstract: We study the limit of the sequence of Kobayashi metrics of Riemann surfaces (when these Riemann surfaces form an analytic fibration in such a way that the total space of fibration becomes a complex surface), as the fibers approach the center fiber which is not in general smooth. We prove that if the total space is a Stein surface and the smooth part of the center fiber contains a component biholomorphic to a quotient of the disk by a Fuchsian group of first kind, then the Kobayashi metrics of the near-by fibers converge to the Kobayashi metric of this component as fibers tend to the center fiber.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1118826-9
PII: S 0002-9947(1993)1118826-9
Article copyright: © Copyright 1993 American Mathematical Society