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June 2011 The Gromov-Hausdorff distances between Alexandrov spaces of curvature bounded below by 1 and the standard spheres
Ayato Mitsuishi
Tsukuba J. Math. 35(1): 1-12 (June 2011). DOI: 10.21099/tkbjm/1311081446

Abstract

Main result in the present paper is the following: If an n-dimensional Alexandrov spaces X n of curvature ≥ 1 has radius greater than Π - ε, then the Gromov-Hausdor. distance between X n and the standard sphere S n is less than τ(ε). Here, τ(ε) is an explicit positive function depending only on ε such that limε→0 τ(ε) = 0. We prove this by using quasigeodesics on Alexandrov spaces.

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Ayato Mitsuishi. "The Gromov-Hausdorff distances between Alexandrov spaces of curvature bounded below by 1 and the standard spheres." Tsukuba J. Math. 35 (1) 1 - 12, June 2011. https://doi.org/10.21099/tkbjm/1311081446

Information

Published: June 2011
First available in Project Euclid: 19 July 2011

zbMATH: 1239.53063
MathSciNet: MR2848813
Digital Object Identifier: 10.21099/tkbjm/1311081446

Subjects:
Primary: 53C20, 53C21

Rights: Copyright © 2011 University of Tsukuba, Institute of Mathematics

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Vol.35 • No. 1 • June 2011
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