This is an announcement for the paper "Some affine invariants revisited" by Alina Stancu.

Abstract: We present several sharp inequalities for the $SL(n)$ invariant $\Omega_{2,n}(K)$ introduced in our earlier work on centro-affine invariants for smooth convex bodies containing the origin. A connection arose with the Paouris-Werner invariant $\Omega_K$ defined for convex bodies $K$ whose centroid is at the origin. We offer two alternative definitions for $\Omega_K$ when $K \in C^2_+$. 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.

Archive classification: math.FA

Mathematics Subject Classification: 52A40, 52A38

Remarks: 15 pages

Submitted from: stancu@mathstat.concordia.ca

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1208.0783

or

http://arXiv.org/abs/1208.0783