Minimal barriers for geometric evolutions

We study some properties of De Giorgi's minimal barriers and local minimal barriers for geometric flows of subsets of R-n. Concerning evolutions of the form partial derivative u/partial derivative t + F(del u, del(2)u) = 0, we prove a representation result for the minimal barrier M(E, F-F) when F is not degenerate elliptic; namely, we show that M(E, F-F) = M(E, FF+), where F+ is the smallest degenerate elliptic function above F. We also characterize the disjoint sets property and the joint sets property in terms of the Function F. (C) 1997 Academic Press.