  We study evolution of manifolds after their creation at high energies.
Several kinds of gravitational Lagrangians with higher derivatives are
considered. It is shown analytically and confirmed numerically that an
asymptotic growth of the maximally symmetric manifolds depends strongly on
their dimensionality. A number of final metrics describing our Universe is
quite poor if we limit ourselves with a maximally symmetric extra space. We
show that the initial conditions can be a reason of nontrivial solutions
(funnels) and study their properties.
