Mahler's lower-bound conjecture for centrally symmetric convex bodies

Let $K\subseteq\mathbb{R}^n$ be a centrally symmetric convex body, and let $K^\circ$ be its polar body. Define the Mahler volume by

$$v(K)=(\operatorname{Vol} K)(\operatorname{Vol} K^\circ).$$

Let $C_n=[-1,1]^n$ be the cube. Mahler's conjecture. In any fixed dimension $n$, $v(K)$ is minimized among centrally symmetric convex bodies by $C_n$.

The conjecture is the lower-bound counterpart to the Blaschke–Santaló inequality, which says that ellipsoids uniquely maximize $v(K)$. The lower bound remains open in general.