  We discuss the inhomogeneous multidimensional mixmaster model in view of
appearing, near the cosmological singularity, a scenario for the dimensional
compactification in correspondence to an 11-dimensional space-time. Our
analysis candidates such a collapsing picture toward the singularity to
describe the actual expanding 3-dimensional Universe and an associated
collapsed 7-dimensional space. To this end, a conformal factor is determined in
front of the 4-dimensional metric to remove the 4-curvature divergences and the
resulting Universe expands with a power-law.inflation. Thus we provide an
additional peculiarity of the eleven space-time dimensions in view of
implementing a geometrical theory of unification.
