Calculus of Variations and Geometric Measure Theory

A. Cesaroni - M. Novaga

$K$ mean-convex and $K$-outward minimizing sets

created by novaga on 25 Nov 2020
modified on 17 Mar 2022


Published Paper

Inserted: 25 nov 2020
Last Updated: 17 mar 2022

Journal: Interfaces Free Bound.
Volume: 24
Number: 1
Pages: 35-61
Year: 2022

ArXiv: 2011.12614 PDF


We consider the evolution of sets by nonlocal mean curvature and we discuss the preservation along the flow of two geometric properties, which are the mean convexity and the outward minimality. The main tools in our analysis are the level set formulation and the minimizing movement scheme for the nonlocal flow. When the initial set is outward minimizing, we also show the convergence of the (time integrated) nonlocal perimeters of the discrete evolutions to the nonlocal perimeter of the limit flow.