Calculus of Variations and Geometric Measure Theory
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A. Cesaroni - M. Novaga

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

created by novaga on 25 Nov 2020
modified on 18 Jun 2021


Accepted Paper

Inserted: 25 nov 2020
Last Updated: 18 jun 2021

Journal: Interfaces Free Bound.
Year: 2020

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.


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