  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.
