The isoperimetrix in the dual Brunn-Minkowski theory

TL;DR

This paper introduces the dual isoperimetrix to address the isoperimetric problem within the dual Brunn-Minkowski theory and explores its relationship with the classical isoperimetrix.

Contribution

It presents the concept of the dual isoperimetrix and establishes its connection to the traditional isoperimetrix in convex geometry.

Findings

Dual isoperimetrix solves the isoperimetric problem in dual Brunn-Minkowski theory

Relationship established between dual and classical isoperimetrix

Advances understanding of dual convex geometric structures

Abstract

We introduce the dual isoperimetrix which solves the isoperimetric problem in the dual Brunn-Minkowski theory. We then show how the dual isoperimetrix is related to the isoperimetrix from the Brunn-Minkowski theory.