Area-expanding embeddings of rectangles

TL;DR

This paper investigates the existence of embeddings between n-dimensional rectangles that uniformly expand k-dimensional areas, providing sharp estimates up to a constant factor across all dimensions.

Contribution

It offers a precise characterization of when such area-expanding embeddings exist between rectangles, with estimates that are sharp up to a constant factor.

Findings

Derived sharp estimates for area-expanding embeddings

Established conditions for embeddings between rectangles

Provided bounds that are tight up to a constant factor

Abstract

We estimate whether there is an embedding from one n-dimensional rectangle into another which expands every k-dimensional area. Our estimate is sharp up to a constant factor in each dimension.