Bi-Lipschitz-equivalent Aleksandrov surfaces, II

Burago, Yu.

doi:10.1090/S1061-0022-05-00885-X

Bi-Lipschitz-equivalent Aleksandrov surfaces, II
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by Yu. Burago
Translated by: the author

St. Petersburg Math. J. 16 (2005), 943-960

DOI: https://doi.org/10.1090/S1061-0022-05-00885-X

Published electronically: November 17, 2005

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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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