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

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

References

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