Examples of Ricci limit spaces with non-integer Hausdorff dimension

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 [ CC00a , Page 15] about collapsing Ricc...

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Bibliographic Details
Published inGeometric and functional analysis Vol. 32; no. 3; pp. 676 - 685
Main Authors Pan, Jiayin, Wei, Guofang
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2022
Springer Nature B.V
Subjects
Analysis
Mathematics
Mathematics and Statistics
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Summary: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 [ CC00a , Page 15] about collapsing Ricci limit spaces.
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ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-022-00598-4