Regularity for Dirac-harmonic maps into certain pseudo-Riemannian manifolds

TL;DR

This paper proves the smoothness of weak Dirac-harmonic maps into stationary Lorentzian manifolds and establishes a regularity theorem for certain critical elliptic systems, advancing understanding in geometric analysis.

Contribution

It introduces new regularity results for Dirac-harmonic maps into pseudo-Riemannian manifolds and extends regularity theory to elliptic systems lacking anti-symmetry.

Findings

Weak Dirac-harmonic maps are smooth into stationary Lorentzian manifolds.

Established regularity for a class of critical elliptic systems without anti-symmetry.

Extended regularity results to broader geometric contexts.

Abstract

We show the smoothness of weakly Dirac-harmonic maps from a closed spin Riemann surface into stationary Lorentzian manifolds, and obtain a regularity theorem for a class of critical elliptic systems without anti-symmetry structures.