The limiting behavior of the kobayashi-royden pseudometric

Research output: Contribution to journalArticle

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 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
Volume339
Issue number1
DOIs
StatePublished - 1993

Fingerprint

Pseudometric
Limiting Behavior
Kobayashi Metric
Fiber
Fibers
Fibration
Riemann Surface
Fuchsian Group
Quotient
Tend
Converge

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

The limiting behavior of the kobayashi-royden pseudometric. / Kaliman, Shulim.

In: Transactions of the American Mathematical Society, Vol. 339, No. 1, 1993, p. 361-371.

Research output: Contribution to journalArticle

@article{38b241b316644edb8a58818afac6b15e,
title = "The limiting behavior of the kobayashi-royden pseudometric",
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 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.",
author = "Shulim Kaliman",
year = "1993",
doi = "10.1090/S0002-9947-1993-1118826-9",
language = "English (US)",
volume = "339",
pages = "361--371",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "1",

}

TY - JOUR

T1 - The limiting behavior of the kobayashi-royden pseudometric

AU - Kaliman, Shulim

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84968518285&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968518285&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1993-1118826-9

DO - 10.1090/S0002-9947-1993-1118826-9

M3 - Article

VL - 339

SP - 361

EP - 371

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 1

ER -