Examples of Ricci limit spaces with non-integer Hausdorff dimension
Differential Geometry
2025-07-17 v2
Abstract
We give the first examples of collapsing Ricci limit spaces on which the Hausdorff dimension of the singular set exceeds that of the regular set; moreover, the Hausdorff dimension of these spaces can be non-integers. This answers a question of Cheeger-Colding about collapsing Ricci limit spaces.
Cite
@article{arxiv.2106.03967,
title = {Examples of Ricci limit spaces with non-integer Hausdorff dimension},
author = {Jiayin Pan and Guofang Wei},
journal= {arXiv preprint arXiv:2106.03967},
year = {2025}
}
Comments
Slightly modified the exposition of the introduction. Added some reference