  We show that, in second-order phase transformations induced by an
inhomogeneous quench, the density of topological defects is drastically
suppressed as the velocity with which the quench propagates becomes smaller
than the speed at which the front of the broken symmetry phase spreads. The
velocity of the broken symmetry phase front is approximately given by the ratio
of the healing length to relaxation time at freeze-out, that is at the instant
when the critical slowing down results in a transition from the adiabatic to
the impulse behavior in the order parameter. Experimental implications are
briefly discussed.
