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Examples of Ricci limit spaces with non-integer Hausdorff dimension

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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 [CC00a, Page 15] about collapsing Ricci limit spaces.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Santa Barbara, CA, USA

    Jiayin Pan

  2. The Fields Institute for Research in Mathematical Sciences, Toronto, Canada

    Jiayin Pan

  3. Department of Mathematics, University of California, Santa Barbara, CA, USA

    Guofang Wei

Authors
  1. Jiayin Pan
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  2. Guofang Wei
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J. Pan was partially supported by AMS Simons travel grant during the preparation of this paper, and is currently supported by Fields Postdoc Fellowship.

G. Wei is partially supported by NSF DMS 1811558, 2104704.

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Pan, J., Wei, G. Examples of Ricci limit spaces with non-integer Hausdorff dimension. Geom. Funct. Anal. 32, 676–685 (2022). https://doi.org/10.1007/s00039-022-00598-4

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  • DOI: https://doi.org/10.1007/s00039-022-00598-4

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