Bi-Lipschitz-equivalent Aleksandrov surfaces, I

A. Belen′Kiĭ; Yu Burago

doi:10.1090/S1061-0022-05-00869-1

Bi-Lipschitz-equivalent Aleksandrov surfaces, I

A. Belen′Kiĭ
, Yu Burago

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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-Lipschitzequivalent 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.

Original language	English (US)
Pages (from-to)	627-638
Number of pages	12
Journal	St. Petersburg Mathematical Journal
Volume	16
Issue number	4
DOIs	https://doi.org/10.1090/S1061-0022-05-00869-1
State	Published - 2005

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1090/S1061-0022-05-00869-1

Cite this

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title = "Bi-Lipschitz-equivalent Aleksandrov surfaces, I",

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-Lipschitzequivalent 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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N2 - In this first paper of two, it is proved that two compact Aleksandrov surfaces with bounded integral curvature and without peak points are bi-Lipschitzequivalent 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.

AB - In this first paper of two, it is proved that two compact Aleksandrov surfaces with bounded integral curvature and without peak points are bi-Lipschitzequivalent 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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U2 - 10.1090/S1061-0022-05-00869-1

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M3 - Article

AN - SCOPUS:85009812167

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EP - 638

JO - St. Petersburg Mathematical Journal

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ER -

Bi-Lipschitz-equivalent Aleksandrov surfaces, I

Abstract

All Science Journal Classification (ASJC) codes

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