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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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Bi-Lipschitz-equivalent Aleksandrov surfaces, I
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by A. Belen′kiĭ and Yu. Burago
Translated by: Yu. D. Burago
St. Petersburg Math. J. 16 (2005), 627-638
DOI: https://doi.org/10.1090/S1061-0022-05-00869-1
Published electronically: June 21, 2005
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Abstract:

In this first paper of two, it is proved that two compact Aleksandrov surfaces with bounded integral curvature and without peak points are bi-Lipschitz-equivalent if they are homeomorphic. Also, conditions under which two tubes with finite negative part of integral curvature are bi-Lipschitz-equivalent are considered. In the second paper an estimate depending only on several geometric characteristics is found for a bi-Lipschitz constant.
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Bibliographic Information
  • A. Belen′kiĭ
  • Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
  • Yu. Burago
  • Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
  • Email: yuburago@pdmi.ras.ru
  • Received by editor(s): September 29, 2003
  • Published electronically: June 21, 2005
  • Additional Notes: The second author was partly supported by grants RFBR 02-01-00090, SS-1914.2003.1, and CRDF RM1-2381-ST-02
  • © Copyright 2005 American Mathematical Society
  • Journal: St. Petersburg Math. J. 16 (2005), 627-638
  • MSC (2000): Primary 53C45
  • DOI: https://doi.org/10.1090/S1061-0022-05-00869-1
  • MathSciNet review: 2090849