On the Homothety Conjecture

Elisabeth M. Werner, Deping Ye

Let $K$ be a convex body in ${\mathbb{R}}^n$ and $\d>0$. The homothety conjecture asks: Does $K_{\d}=c K$ imply that $K$ is an ellipsoid? Here $K_{\d}$ is the (convex) floating body and $c…