On an extension of the Blaschke-Santalo inequality and the hyperplane conjecture

摘要

Let K be a symmetric convex body and K degrees its polar body. Call phi(K) = 1/vertical bar K vertical bar vertical bar K degrees vertical bar integral(K)integral(K degrees) (x, y)(2) dydx. It is conjectured that phi (K) is maximum when K is an ellipsoid. In particular this statement implies the Blaschke-Santalo inequality and the hyperplane conjecture. We verify this conjecture when K is restricted to be a p-ball. (C) 2008 Elsevier Inc. All rights reserved.