We study conformal theories of gravity, i.e. those whose action is invariant
under the local transformation g_{\mu\nu} -> \omega^2 (x) g_{\mu\nu}. As is
well known, in order to obtain Einstein gravity in 4D it is necessary to
introduce a scalar compensator with a VEV that spontaneously breaks the
conformal invariance and generates the Planck mass. We show that the
compactification of extra dimensions in a higher dimensional conformal theory
of gravity also yields Einstein gravity in lower dimensions, without the need
to introduce the scalar compensator. It is the field associated with the size
of the extra dimensions (the radion) who takes the role of the scalar
compensator in 4D. The radion has in this case no physical excitations since
they are gauged away in the Einstein frame for the metric. In these models the
stabilization of the size of the extra dimensions is therefore automatic.Comment: 13 page