  Employing a centro-affine flow on smooth convex bodies, we generate new
centro-affine differential invariants. One class of the newly defined
invariants is the object of a sharp isoperimetric inequality, while other new
inequalities on known centro-affine invariants are obtained as a byproduct of
the flow's study. Furthermore, this approach led to a geometric interpretation
of a new affine surface area recently introduced by Ludwig and Reitzner.
