The Santal贸-regions of a convex body
The Santal贸-regions of a convex body
Motivated by the Blaschke-Santal贸 inequality, we define for a convex body $K$ in $\mathbf {R}^n$ and for $t \in \mathbf {R}$ the Santal贸-regions $S(K,t)$ of $K$. We investigate the properties of these sets and relate them to a concept of affine differential geometry, the affine surface area of $K$.