Minimal Barriers for Geometric Evolutions

We study some properties of De Giorgiʹs minimal barriers and local minimal barriers for geometric flows of subsets ofRn. Concerning evolutions of the form ∂u/∂t+F( u, 2u)=0, we prove a representation result for the minimal barrier (E, F) whenFis not degenerate elliptic; namely, we show that (E, F)= (E, F+), whereF+is the smallest degenerate elliptic function aboveF. We also characterize the disjoint sets property and the joint sets property in terms of the functionF.