$p$-Dirac Operators

TL;DR

This paper introduces non-linear $p$-Dirac operators related to the $p$-harmonic equation, extending their definition to spin manifolds and the sphere, broadening the scope of Dirac operator applications.

Contribution

It presents the first formulation of non-linear $p$-Dirac operators and extends their framework to various geometric contexts.

Findings

Defined non-linear $p$-Dirac operators in Euclidean space.

Extended the operators to spin manifolds and the sphere.

Provided foundational groundwork for future research in non-linear Dirac analysis.

Abstract

We introduce non-linear Dirac operators in $\mathbb{R}^{n}$ associated to the $p$-harmonic equation and we extend to other contexts including spin manifolds and the sphere.