## The limiting behavior of the Kobayashi-Royden pseudometric

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- by Shulim Kaliman PDF
- Trans. Amer. Math. Soc.
**339**(1993), 361-371 Request permission

## 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.## References

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## Additional 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