On counterexamples in questions of unique determination of convex bodies

TL;DR

This paper presents a construction that provides counterexamples to longstanding questions about whether convex bodies can be uniquely determined by certain geometric data.

Contribution

It introduces a novel construction method that demonstrates the failure of unique determination in convex geometry.

Findings

Counterexamples to uniqueness questions in convex body determination

Highlights limitations of existing geometric data for unique identification

Provides new insights into convex geometric analysis

Abstract

We discuss a construction that gives counterexamples to various questions of unique determination of convex bodies.