Nonlinear Dirac equations on Riemann surfaces

Abstract

We have developed 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 have provided the key analytical steps, i.e., small energy regularity and removable singularity theorems and energy identities for solutions.