Some Affine Invariants Revisited

Abstract

We present several sharp inequalities for the SL(n) invariant Ω2, n(K) introduced in our earlier work on centro-affine invariants for smooth convex bodies containing the origin. A connection arose with the Paouris-Werner invariant ΩKdefined for convex bodies K whose centroid is at the origin. We offer two alternative definitions for ΩKwhen K ∈ C+2. The technique employed prompts us to conjecture that any SL(n) invariant of convex bodies with continuous and positive centro-affine curvature function can be obtained as a limit of normalized p-affine surface areas of the convex body. © Springer Science+Business Media New York 2013.