Modified Shephard's problem on projections of convex bodies

TL;DR

This paper disproves a conjecture by Koldobsky, showing that comparing (n-2)-derivatives of projection functions of symmetric convex bodies is insufficient for the Shephard problem in all dimensions.

Contribution

It provides a counterexample to Koldobsky's conjecture, advancing understanding of projection functions in convex geometry.

Findings

Disproved Koldobsky's conjecture on projection derivatives

Showed limitations of derivative comparisons in Shephard's problem

Enhanced knowledge of convex body projection properties

Abstract

We disprove a conjecture of A. Koldobsky asking whether it is enough to compare $(n-2)$-derivatives of the projection functions of two symmetric convex bodies in the Shephard problem in order to get a positive answer in all dimensions.