Asymptotic geometric regularity of CAT(0) spaces
Differential Geometry
2026-02-25 v1 Metric Geometry
Abstract
We prove that if an n-dimensional geodesically complete CAT(0) space has Tits boundary sufficiently close to the (n-1)-dimensional standard unit sphere, then it is bi-Lipschiz homeomorphic to the n-dimensional Euclidean space. As an application, we conclude that if an (n-1)-dimensional geodesically complete CAT(1) space is sufficiently close to the (n-1)-dimensional standard unit sphere, then they are bi-Lipschiz homeomorphic to each other.
Keywords
Cite
@article{arxiv.2602.20533,
title = {Asymptotic geometric regularity of CAT(0) spaces},
author = {Koichi Nagano},
journal= {arXiv preprint arXiv:2602.20533},
year = {2026}
}
Comments
21 pages. arXiv admin note: substantial text overlap with arXiv:2601.22673