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Bi-Lipschitz-equivalent Aleksandrov surfaces, I

Authors: A. Belen'kii and Yu. Burago
Translated by: Yu. D. Burago
Original publication: Algebra i Analiz, tom 16 (2004), nomer 4.
Journal: St. Petersburg Math. J. 16 (2005), 627-638
MSC (2000): Primary 53C45
Published electronically: June 21, 2005
MathSciNet review: 2090849
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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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Additional Information

A. Belen'kii
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

Keywords: Two-dimensional manifold of bounded integral curvature, Lipschitz metric, comparison triangle.
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
Article copyright: © Copyright 2005 American Mathematical Society

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