Uniqueness of radial centers of parallel bodies

We show the uniqueness of the radial centers of any order $\alpha$ of a parallel body of a convex body $\Omega$ in $\mathbb R^m$ at distance $\delta$ if $\delta$ is greater than the diameter of $\Omega$ multiplied by a constant which depends only on the dimension $m$.

Author: Jun O'Hara

Source: https://archive.org/