On an extension of the Blaschke-Santalo inequality

Details On an extension of the Blaschke-Santalo inequality On an extension of the Blaschke-Santalo inequality

2007-10-31

arxiv.org/abs/0710.5907v1

Mathematics

Functional Analysis

7 pages

Scientific paper

Let $K$ be a convex body and $K^\circ$ its polar body. Call
$\phi(K)=\frac{1}{|K||K^\circ|}\int_K\int_{K^\circ}< x,y>^2 dxdy$. It is
conjectured that $\phi(K)$ 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.

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