On a theorem of D. Ryabogin and V. Yaskin about detecting symmetry

TL;DR

This paper provides a straightforward proof of a recent theorem on identifying symmetry in star-shaped bodies in Euclidean space using conical section functions, building on an earlier theorem by the authors.

Contribution

It offers a simplified deduction of a recent symmetry detection theorem for star bodies, connecting it to previous work by the authors.

Findings

Simplified proof of the symmetry detection theorem

Connection between conical section functions and symmetry

Extension of previous theoretical results

Abstract

We give a simple deduction of a recent theorem of D. Ryabogin and V. Yaskin, about detecting symmetry of star bodies in ${\Bbb{R}}^n$ with $C^1$ radial functions --- via their conical section functions --- from an older theorem of us.