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Bi-Lipschitz-equivalent Aleksandrov surfaces, I
Author(s):
A.
Belen'kii;
Yu.
Burago
Translated by:
Yu. D. Burago
Original publication:
Algebra i Analiz,
tom 16
(2004),
vypusk 4.
Journal:
St. Petersburg Math. J.
16
(2005),
627-638.
MSC (2000):
Primary 53C45
Posted:
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.
References:
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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
Email:
yuburago@pdmi.ras.ru
DOI:
10.1090/S1061-0022-05-00869-1
PII:
S 1061-0022(05)00869-1
Keywords:
Two-dimensional manifold of bounded integral curvature,
Lipschitz metric,
comparison triangle.
Received by editor(s):
29/SEP/2003
Posted:
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 of article:
Copyright
2005,
American Mathematical Society
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