Calculus of Variations and Geometric Measure Theory

F. Fiorani - A. Mondino - D. Semola

Monotonicity formula and stratification of the singular set of perimeter minimizers in RCD spaces

created by mondino on 14 Jul 2023



Inserted: 14 jul 2023
Last Updated: 14 jul 2023

Year: 2023

ArXiv: 2307.06205 PDF


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.