**Inserted:** 4 dec 1996

**Year:** 1996

**Abstract:**

We prove that the minimal barriers in the sense of De Giorgi are equivalent to the viscosity solutions for fully nonlinear parabolic geometric problems of the form ut + F(t, x, grad u, grad2u) =0, under the assumptions on F made by Giga-Goto-Ishii-Sato in a recent paper. More generally, we prove that the minimal barrier is the maximal between all viscosity subsolutions assuming a given initial datum. All results can be extended to the case in which F is not degenerate elliptic, provided that also F+, which is defined as the smallest degenerate elliptic function above F, satisfies the assumptions of Giga-Goto-Ishii-Sato.