Global existence of Dirac-wave maps with curvature term on expanding spacetimes

TL;DR

This paper establishes the global existence of Dirac-wave maps with curvature terms and wave maps on expanding spacetimes, under small initial data and certain growth conditions, advancing understanding of these geometric PDEs.

Contribution

It provides the first global existence results for Dirac-wave maps with curvature terms on expanding spacetimes, extending previous work on wave maps.

Findings

Global existence of Dirac-wave maps with curvature term

Global existence of wave maps under similar conditions

Results hold on arbitrary dimensional globally hyperbolic manifolds

Abstract

We prove the global existence of Dirac-wave maps with curvature term with small initial data on globally hyperbolic manifolds of arbitrary dimension which satisfy a suitable growth condition. In addition, we also prove a global existence result for wave maps under similar assumptions.