Mark Meyer

Norm rigidity and equality cases for the Dyn--Farkhi inequality

For a convex body $K\subset\mathbb{R}^2$ that is symmetric with respect to the origin, and for a nonempty set $S\subset\mathbb{R}^2$, we study the $K$-Hausdorff distance from convex hull, defined by \begin{align*} d^{(K)}(S):=\sup_{x\in \text{conv}(S)}\inf_{s\in S}\|x-s\|_K, \end{align*} where $\|\cdot \|_K$ is the nor...