2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135243We develop analytical methods for nonlinear Dirac equations. Examples of such equations include Dirac-harmonic maps with curvature term and the equations describing the generalized Weierstrass representation of surfaces in three-manifolds. We provide the key analytical steps, i.e., small energy regularity and removable singularity theorems and energy identities for solutions.to appear in Annals of Global Analysis and GeometryDifferential GeometryAnalysis of PDEs58J05, 53C27text