Lipschitzness of the width and diameter functions of convex bodies in $\mathbb R^n$

TL;DR

This paper derives Lipschitz constants for the width and diameter functions of convex bodies in high-dimensional spaces, relating them to the body's diameter and thickness, and introduces a dual approach to thickness.

Contribution

It provides explicit Lipschitz constants for width and diameter functions based on geometric parameters and proposes a dual method for analyzing thickness.

Findings

Lipschitz constants expressed in terms of diameter and thickness

A dual approach to the concept of thickness

Enhanced understanding of convex body geometry in $\

Abstract

Lipschitz constants for the width and diameter functions of a convex body in $\mathbb R^n$ are found in terms of its diameter and thickness (maximum and minimum of both functions). Also, a dual approach to thickness is proposed.