Stretching multifractal spectra and area compression of homeomorphisms with integrable distortion in higher dimensions

TL;DR

This paper investigates the behavior of homeomorphisms with integrable distortion in higher dimensions, providing sharper bounds for area compression by analyzing their stretching multifractal spectra.

Contribution

It introduces improved bounds for area compression of such homeomorphisms through new estimates of their stretching multifractal spectra.

Findings

Sharper bounds for area compression in higher dimensions

Development of sharp estimates for stretching multifractal spectra

Extension of previous results by Clop and Herron

Abstract

We consider homeomorphisms with integrable distortion in higher dimensions and sharpen the previous bound for area compression, which was presented by Clop and Herron. Our method relies on developing sharp bounds for the stretching multifractal spectra of these mappings.