Preprint

Inserted: 14 jul 2023
Last Updated: 14 jul 2023

Year: 2023

Abstract:

The goal of this paper is to establish a monotonicity formula for perimeter minimizing sets in RCD(0,N) metric measure cones, together with the associated rigidity statement. The applications include sharp Hausdorff dimension estimates for the singular strata of perimeter minimizing sets in non collapsed RCD spaces and the existence of blow-down cones for global perimeter minimizers in Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth.

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• FioraniMondinoSemola.pdf