Centro-Affine Invariants for Smooth Convex Bodies

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