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

  • Francesco Fiorani

    University of Oxford, Oxford, UK
  • Andrea Mondino

    University of Oxford, Oxford, UK
  • Daniele Semola

    ETH Zürich, Zürich, Switzerland
Monotonicity formula and stratification of the singular set of perimeter minimizers in RCD spaces cover
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Abstract

The goal of this paper is to establish a monotonicity formula for perimeter minimizing sets in 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 spaces and the existence of blow-down cones for global perimeter minimizers in Riemannian manifolds with non-negative Ricci curvature and Euclidean volume growth.

Cite this article

Francesco Fiorani, Andrea Mondino, Daniele Semola, Monotonicity formula and stratification of the singular set of perimeter minimizers in RCD spaces. Comment. Math. Helv. (2025), published online first

DOI 10.4171/CMH/598