Asian Journal of Mathematics

Volume 17 (2013)

Number 4

A new proof of almost isometry theorem in Alexandrov geometry with curvature bounded below

Pages: 715 – 728

DOI: https://dx.doi.org/10.4310/AJM.2013.v17.n4.a9

Authors

Xiaole Su (School of Mathematical Sciences (and Lab. Math. Com. Sys.), Beijing Normal University, Beijing, China)

Hongwei Sun (School of Mathematical Sciences, Capital Normal University, Beijing, China)

Yusheng Wang (School of Mathematical Sciences (and Lab. Math. Com. Sys.), Beijing Normal University, Beijing, China)

Abstract

In this paper we give a new proof (along the line of the original proof) for the almost isometry theorem in Alexandrov geometry with curvature bounded below in [1]. The motivation of the new proof is that we find that Lemma 9.11 in [1] is incorrect (see Example 1.3 below), while this lemma is a crucial step in the original proof.

Keywords

Alexandrov spaces, GH-approximation, almost isometry

2010 Mathematics Subject Classification

53C20

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Published 27 December 2013