Article ID Journal Published Year Pages File Type
4621007 Journal of Mathematical Analysis and Applications 2008 9 Pages PDF
Abstract

Let K   be a symmetric convex body and K○K○ its polar body. Callϕ(K)=1|K||K○|∫K∫K○〈x,y〉2dydx. It is conjectured that ϕ(K)ϕ(K) is maximum when K is an ellipsoid. In particular this statement implies the Blaschke–Santaló inequality and the hyperplane conjecture. We verify this conjecture when K is restricted to be a p-ball.

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Physical Sciences and Engineering Mathematics Analysis
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