On the duality of moduli in arbitrary codimension

TL;DR

This paper investigates the duality properties of moduli of slices in Euclidean n-cubes across arbitrary codimensions, establishing an optimal upper bound for their relationship.

Contribution

It introduces a new duality framework for moduli of slices in Euclidean cubes and proves the optimal upper bound for their duality relationship.

Findings

Established the duality of moduli for slices of Euclidean n-cubes.

Proved the optimal upper bound of 1 for the duality relationship.

Provides theoretical insights into geometric measure theory in high dimensions.

Abstract

We study the duality of moduli of k- and (n-k)-dimensional slices of euclidean n-cubes, and establish the optimal upper bound 1.