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arXiv · 2309.14762

GH-convergence of CAT$(0)$-spaces: stability of the Euclidean factor

Nicola Cavallucci
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Abstract

We prove that if a sequence of geodesically complete CAT$(0)$-spaces $X_j$ with uniformly cocompact discrete groups of isometries converges in the Gromov-Hausdorff sense to $X_\infty$, then the dimension of the maximal Euclidean factor splitted off by $X_\infty$ and $X_j$ is the same, for $j$ big enough. In other words, no additional Euclidean factors can appear in the limit.

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Nicola Cavallucci. 2023-09-26. GH-convergence of CAT$(0)$-spaces: stability of the Euclidean factor. https://arxiv.org/abs/2309.14762

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