The limiting behavior of the kobayashi-royden pseudometric

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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 thesmooth 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.d.

Original languageEnglish (US)
Pages (from-to)361-371
Number of pages11
JournalTransactions of the American Mathematical Society
Issue number1
StatePublished - Sep 1993

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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