Lipschitz Gromov-Hausdorff approximations to two-dimensional closed piecewise flat Alexandrov spaces

doi:10.1007/s11464-019-0762-z

Front. Math. China

2019, Vol. 14

Issue (2) : 349-380 https://doi.org/10.1007/s11464-019-0762-z

RESEARCH ARTICLE

Lipschitz Gromov-Hausdorff approximations to two-dimensional closed piecewise flat Alexandrov spaces

Xueping LI(

)

Department of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China

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Abstract

We show that a closed piecewise flat 2-dimensional Alexandrov space Σ can be bi-Lipschitz embedded into a Euclidean space such that the embedded image of Σ has a tubular neighborhood in a generalized sense. As an application, we show that for any metric space sufficiently close to Σ in the Gromov-Hausdorff topology, there is a Lipschitz Gromov-Hausdorff approxima-tion.

Keywords Alexandrov space Gromov-Hausdorff approximation tubular neighborhood

Corresponding Author(s): Xueping LI

Issue Date: 14 May 2019

Cite this article:

Xueping LI. Lipschitz Gromov-Hausdorff approximations to two-dimensional closed piecewise flat Alexandrov spaces[J]. Front. Math. China, 2019, 14(2): 349-380.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0762-z
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I2/349

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