Volume product of planar polar convex bodies --- lower estimates with stability

K. J. Böröczky, E. Makai, M. Meyer +1

Let $K\subset {\mathbb{R}}^2$ be an $o$-symmetric convex body, and $K^{\ast }$ its polar body. Then we have $|K|\cdot |K^{\ast }|\ge 8$, with equality if and only if $K$ is a parallelogram. (…