Area-expanding embeddings of rectangles
Larry Guth

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.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Geometric and Algebraic Topology · Mathematical Dynamics and Fractals
