On the dimension of the singular set of perimeter minimizers in spaces with a two-sided Ricci curvature bound

2024/05/09 by Cucinotta, Alessandro, Fiorani, Francesco
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.05775

Abstract

We show that the Hausdorff dimension of the singular set of perimeter minimizers in non-collapsed Ricci limit spaces with a two-sided Ricci curvature bound is at most N-5, where N is the dimension of the ambient space. The estimate is sharp.

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