Examples of Ricci limit spaces with non-integer Hausdorff dimension

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.

Slightly modified the exposition of the introduction. Added some reference

References in corpus (1)

• Conjectures and Open Questions on the Structure and Regularity of Spaces with Lower Ricci Curvature Bounds

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