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arXiv · 0710.5907

On an extension of the Blaschke-Santalo inequality

David Alonso-Gutierrez
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Abstract

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

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David Alonso-Gutierrez. 2007-10-31. On an extension of the Blaschke-Santalo inequality. https://arxiv.org/abs/0710.5907

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