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arXiv · 2602.20533

Asymptotic geometric regularity of CAT(0) spaces

Koichi Nagano
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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.

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Koichi Nagano. 2026-02-24. Asymptotic geometric regularity of CAT(0) spaces. https://arxiv.org/abs/2602.20533

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