Pointwise rotation for mappings with exponentially integrable distortion

TL;DR

This paper establishes an upper bound on the pointwise rotation of mappings with exponentially integrable distortion and demonstrates that this bound is essentially optimal through explicit examples.

Contribution

It introduces a sharp upper bound for pointwise rotation in mappings with p-exponentially integrable distortion, supported by examples attaining this bound.

Findings

Derived an upper bound for pointwise rotation.

Constructed examples showing the bound's optimality.

Enhanced understanding of distortion effects in geometric mappings.

Abstract

We prove an upper bound for pointwise rotation of mappings with $p$-exponentially integrable distortion. We also show that this bound is essentially optimal by providing examples which attain this rotation up to a constant multiplication.