Singular Weyl's law with Ricci curvature bounded below

Authors:
  • XDXianche Dai
    Xianche Dai
  • SHShouhei Honda
    Shouhei Honda
  • JPJiayin Pan
    Jiayin Pan
  • GWGuofang Wei
    Guofang Wei
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Abstract
Using the examples constructed by the last two authors, we show that for compact $\mathrm{RCD}(K,N)$/Ricci limit spaces, Weyl's law may not hold for any power, and in the case when power law holds, it is in terms of the Hausdorff measure of the singular set instead of the regular set. These are the first examples with such features.