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Bi-Lipschitz-equivalent Aleksandrov surfaces, II
Author(s):
Yu.
Burago
Translated by:
the author
Original publication:
Algebra i Analiz,
tom 16
(2004),
vypusk 6.
Journal:
St. Petersburg Math. J.
16
(2005),
943-960.
MSC (2000):
Primary 53C45
Posted:
November 17, 2005
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Additional information
Abstract:
It is proved that any two homeomorphic closed Aleksandrov surfaces of bounded integral curvature are bi-Lipschitz-equivalent with constant depending only on their Euler number, upper bounds for their diameters and negative integral curvatures, and two positive numbers  and  such that each loop of length at most  bounds a disk of positive curvature at most  .
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Additional Information:
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/S1061-0022-05-00885-X
PII:
S 1061-0022(05)00885-X
Keywords:
Bi-Lipschitz map,
two-dimensional manifold,
bounded integral curvature,
Aleksandrov surface
Received by editor(s):
16/MAR/2004
Posted:
November 17, 2005
Additional Notes:
This work was partially supported by grants RFBR 02-01-00090, SS-1914.2003.1, CRDF RM1-2381-ST-02, and by the Shapiro Foundation of Pennsylvania State University
Copyright of article:
Copyright
2005,
American Mathematical Society
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