  Using Perelman's approach for geometrical flows in terms of an entropy
functional, the Higgs mechanism is studied dynamically along flows defined in
the space of parameters and in fields space. The model corresponds to
two-dimensional gravity that incorporates torsion as the gradient of a Higgs
field, and with the reflection symmetry to be spontaneously broken. The results
show a discrete mass spectrum, and the existence of a mass gap between the
Unbroken Exact Symmetry and the Spontaneously Broken Symmetry scenarios. In the
later scenario, the geometries at the degenerate vacua correspond to
conformally flat manifolds without torsion; twisted two-dimensional geometries
are obtained by building perturbation theory around a ground state; the
tunneling quantum probability between vacua is determined along the flows.
