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Bi-Lipschitz-equivalent Aleksandrov surfaces, II


Author: Yu. Burago
Translated by: the author
Original publication: Algebra i Analiz, tom 16 (2004), nomer 6.
Journal: St. Petersburg Math. J. 16 (2005), 943-960
MSC (2000): Primary 53C45
DOI: https://doi.org/10.1090/S1061-0022-05-00885-X
Published electronically: November 17, 2005
MathSciNet review: 2117448
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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 $ \varepsilon$ and $ l$ such that each loop of length at most $ l$ bounds a disk of positive curvature at most $ 2\pi-\varepsilon$.


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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: https://doi.org/10.1090/S1061-0022-05-00885-X
Keywords: Bi-Lipschitz map, two-dimensional manifold, bounded integral curvature, Aleksandrov surface
Received by editor(s): March 16, 2004
Published electronically: 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
Article copyright: © Copyright 2005 American Mathematical Society

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