English

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.

Keywords

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