Centro-affine invariants for smooth convex bodies (Q2889567)

This paper starts with the definition of the centro-affine flow and several of its properties. Then the author recalls the definition of \(L_{p}\) affine surface areas, \(\Omega_{p}\), and list several inequalities for them implied by the flow. The fourth section states the main result defining the new centro-affine invariants and proves a sharp isoperimetric inequality for a class of such invariants. In the last section, the author shows a geometric interpretation of the \(L_{\phi }\) affine surface area introduced by Ludwig and Reitzner.