On an extension of the Blaschke-Santalo inequality

David Alonso-Gutierrez

Let $K$ be a convex body and $K^{\circ }$ its polar body. Call $\varphi (K)=\frac{1}{|K||K^{\circ }|}{\int }_K{\int }_{K^{\circ }}<x,y{>}^{2}dxdy$. It is conjectured that $\varphi (K)$ is maximum when $K$ is the…