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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The limiting behavior of the Kobayashi-Royden pseudometric
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by Shulim Kaliman
Trans. Amer. Math. Soc. 339 (1993), 361-371
DOI: https://doi.org/10.1090/S0002-9947-1993-1118826-9
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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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Bibliographic Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 339 (1993), 361-371
  • MSC: Primary 32H15; Secondary 30F45, 32E10, 32G10
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1118826-9
  • MathSciNet review: 1118826