Examples of $CD(0,N)$ spaces with non-constant dimension
Metric Geometry
2023-10-10 v1 Differential Geometry
Abstract
In this work, we generalize the results obtained in (J. Geom. Anal., 32(6):Paper No.173, 32, 2022), presenting some examples of spaces having different dimensions in different regions, deducing in particular that the topological splitting may fail in spaces. We also observe that any reasonable non-branching condition may fail in spaces and that the existence of an optimal transport map, between two absolutely continuous marginals, is not guaranteed by the condition, without requiring a non-branching assumption. Moreover, we show that the strict condition is strictly stronger than the classical one and it is not stable with respect to the measured Gromov-Hausdorff convergence.
Keywords
Cite
@article{arxiv.2310.05738,
title = {Examples of $CD(0,N)$ spaces with non-constant dimension},
author = {Mattia Magnabosco},
journal= {arXiv preprint arXiv:2310.05738},
year = {2023}
}