On the Dimension of the Singular Set of Perimeter Minimizers in Spaces with a Two-Sided Bound on the Ricci Curvature

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2024年10月23日

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Alessandro Cucinotta,
Francesco Fiorani

摘要

We show that the Hausdorff dimension of the singular set of perimeter minimizers in noncollapsed limits of manifolds with two-sided bounds on the Ricci curvature is at most $n-5$ $n - 5$ , where n is the dimension of the ambient space. The estimate is sharp.