2007/10/31 by David Alonso–Gutiérrez, Alonso-Gutierrez, David
Mathematics · #Point processes and geometric inequalities #Mathematical Inequalities and Applications #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.0710.5907
Let K be a convex body and K^∘ its polar body. Call ϕ(K)=(1)/(|K||K^∘|)∫K∫K^∘< x,y>2 dxdy. It is conjectured that ϕ(K) is maximum when K is the euclidean ball. In particular this statement implies the Blaschke-Santalo inequality. We verify this conjecture when K is restricted to be a p--ball.