Directional isoperimetric inequalities and rational homotopy invariants

TL;DR

This paper introduces a new directional isoperimetric inequality to estimate second order linking invariants of Lipschitz maps, leading to novel lower bounds on k-dilation between ellipses.

Contribution

It develops a directionally-dependent isoperimetric inequality and applies it to derive new bounds on k-dilation for maps between ellipses, advancing geometric analysis tools.

Findings

New lower bounds for k-dilation of Lipschitz maps between ellipses

A novel directionally-dependent isoperimetric inequality

Estimates of second order linking invariants

Abstract

We estimate the second order linking invariants of Lipschitz maps from an n-dimensional ellipse. The estimate uses a new directionally-dependent version of the isoperimetric inequality for cycles inside the ellipse. Using this work, we prove new lower bounds for the k-dilation of maps from one ellipse to another.