### 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 language | English (US) |
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Pages (from-to) | 361-371 |

Number of pages | 11 |

Journal | Transactions of the American Mathematical Society |

Volume | 339 |

Issue number | 1 |

DOIs | |

State | Published - 1993 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

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

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 339, no. 1, pp. 361-371. https://doi.org/10.1090/S0002-9947-1993-1118826-9

}

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 -