Metric stability of trees and tight spans
Metric Geometry
2013-03-28 v1
Abstract
In this note, we prove optimal extension results for roughly isometric relations between metric (R-)trees and injective metric spaces. This yields sharp stability estimates, in terms of the Gromov-Hausdorff (GH) distance, for certain metric spanning constructions: The GH distance of two metric trees spanned by some subsets is smaller than or equal to the GH distance of these sets. The GH distance of the injective hulls, or tight spans, of two metric spaces is at most twice the GH distance between themselves.
Keywords
Cite
@article{arxiv.1303.6826,
title = {Metric stability of trees and tight spans},
author = {Urs Lang and Maël Pavón and Roger Züst},
journal= {arXiv preprint arXiv:1303.6826},
year = {2013}
}
Comments
8 pages, 1 figure