Asymptotic behavior for singularities of the mean curvature flow

9 n > 1, be a compact -dimensional manifold without boundary and assume that Fo: M n -> U n+{ smoothly immerses M n as a hypersurface in a Euclidean (n + l)-space R +1 . We say that MQ = F 0 (Af") is moved along its mean curvature vector if there is a whole family F( , t) of smooth immersions with corresponding hypersurfaces M t = F( , t)(M n ) such that