Published Paper

Inserted: 14 jul 2023
Last Updated: 17 mar 2026

Journal: Comment. Math. Helv.
Volume: 101
Number: 2
Pages: 193--238
Year: 2026
Doi: DOI 10.4171/CMH/598

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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