Examples of Ricci limit spaces with non-integer Hausdorff dimension

2021/06/07 by Jiayin Pan, Pan, Jiayin, Guofang Wei +1 · 1 citation
Computer Science · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · doi:10.48550/arxiv.2106.03967

openalex publication_date 2021/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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