Uniqueness of radial centers of parallel bodies

Abstract

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 $m$.

13 pages, 8 figures

References in corpus (1)

• Renormalization of potentials and generalized centers

Cited by in corpus (2)

• Stationary radial centers and characterization of convex polyhedrons
• Experimental investigation on the uniqueness of a center of a body