2012/08/03 by Alina Stancu, Stancu, Alina
Biochemistry, Genetics and Molecular Biology · Mathematics · #52A38 #52A40 #Dermatological and Skeletal Disorders #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1208.0783
openalex publication_date 2012/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ΩK defined for convex bodies K whose centroid is at the origin. We offer two alternative definitions for ΩK when K ∈ C2+. 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.