Quasiconformal extension fields

TL;DR

This paper investigates quasiconformal extension fields, establishing a lower energy bound based on topological degree, and explores the minimization of q-harmonic energy, demonstrating higher integrability of minimizers.

Contribution

It introduces a lower energy bound for quasiconformal extension fields and analyzes the higher integrability of energy minimizers in the context of q-harmonic energy.

Findings

Lower energy bound in terms of topological degree

Existence of higher integrability for minimizers

Analysis of q-harmonic energy minimization

Abstract

We consider extensions of differential fields of mappings and obtain a lower energy bound for quasiconformal extension fields in terms of the topological degree. We also consider the related minimization problem for the $q$-harmonic energy, and show that the energy minimizers admit higher integrability.