Invertible harmonic mappings, beyond Kneser

TL;DR

This paper extends classical criteria for invertibility of planar harmonic mappings, providing necessary and sufficient conditions that generalize the Radó-Kneser-Choquet theorem, thereby broadening understanding of harmonic map invertibility.

Contribution

It introduces generalized criteria for invertibility of harmonic mappings that go beyond the classical Kneser conditions, offering a more comprehensive theoretical framework.

Findings

Established necessary and sufficient invertibility criteria

Generalized the Radó-Kneser-Choquet theorem

Enhanced understanding of harmonic map invertibility

Abstract

We prove necessary and sufficient criteria of invertibility for planar harmonic mappings which generalize a classical result of H. Kneser, also known as the Rad\'{o}-Kneser-Choquet theorem.