Nonlinear Dirac equations on Riemann surfaces

Abstract

We 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 Geometry

References in corpus (2)

• Two-dimensional Dirac operator and surface theory
• The first conformal Dirac eigenvalue on 2-dimensional tori