Asian Journal of Mathematics

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

Yusheng Wang, Xiaole Su, and Hongwei Sun

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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 Yu. Burago, M. Gromov, and G. Perel’man, A. D. Alexandrov spaces with curvature bounded below, Russian Math. Surveys, 47:2 (1992), pp. 1–58. The motivation of the new proof is that we find that Lemma 9.11 in A. D. Alexandrov spaces with curvature bounded below is incorrect (see Example 1.3 below), while this lemma is a crucial step in the original proof.

Article information

Source
Asian J. Math., Volume 17, Number 4 (2013), 715-728.

Dates
First available in Project Euclid: 22 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1408712351

Mathematical Reviews number (MathSciNet)
MR3152261

Zentralblatt MATH identifier
1316.53081

Subjects
Primary: 53-C20

Keywords
Alexandrov spaces GH-approximation almost isometry

Citation

Wang, Yusheng; Su, Xiaole; Sun, Hongwei. A new proof of almost isometry theorem in Alexandrov geometry with curvature bounded below. Asian J. Math. 17 (2013), no. 4, 715--728. https://projecteuclid.org/euclid.ajm/1408712351


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