Homotopy of area decreasing maps by mean curvature flow

Let f:M→Nf:M→N be a smooth area decreasing map between two Riemannian manifolds (M,gM)(M,gM) and (N,gN)(N,gN). Under weak and natural assumptions on the curvatures of (M,gM)(M,gM) and (N,gN)(N,gN), we prove that the mean curvature flow provides a smooth homotopy of f to a constant map.