The Andoni-Naor-Neiman inequalities and isometric embeddability into a CAT(0) space
Metric Geometry
2026-04-09 v4
Abstract
Andoni, Naor and Neiman (2018) established a family of quadratic metric inequalities that hold true in every CAT(0) space. As stated in their paper, this family seems to include all previously used quadratic metric inequalities that hold true in every CAT(0) space. We prove that there exists a metric space that satisfies all inequalities in this family but does not admit an isometric embedding into any CAT(0) space. More precisely, we prove that the 6-point metric space constructed by Nina Lebedeva, which does not admit an isometric embedding into any CAT(0) space, satisfies all inequalities in this family.
Keywords
Cite
@article{arxiv.2404.13871,
title = {The Andoni-Naor-Neiman inequalities and isometric embeddability into a CAT(0) space},
author = {Tetsu Toyoda},
journal= {arXiv preprint arXiv:2404.13871},
year = {2026}
}
Comments
17 pages. Published online in Journal of Topology and Analysis