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

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