  We study the mean curvature flow of hypersurfaces in $\R^{n+1}$, with initial
surfaces sufficiently close to the standard $n$-dimensional sphere. The
closeness is in the Sobolev norm with the index greater than $\frac{n}{2}+1$
and therefore it does not impose restrictions of the mean curvature of the
initial surface. We show that the solution of such a flow collapses to a point,
$z_*$, in a finite time, $t_*$, approaching exponentially fast the spheres of
radii $\sqrt{2n(t_*-t)}$, centered at $z(t)$, with the latter converging to
$z_*$.
  Keywords: mean curvature flow, evolution of surfaces, collapse of surfaces,
asymptotic stability, asymptotic dynamics, dynamics of surfaces, mean curvature
soliton, nonlinear parabolic equation.
