Nonlinear Dirac equations on Riemann surfaces
Qun Chen, Jürgen Jost, and Guofang Wang
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Submission date: 24. Apr. 2007
published in: Annals of global analysis and geometry, 33 (2008) 3, p. 253-270
DOI number (of the published article): 10.1007/s10455-007-9084-6
MSC-Numbers: 58J05, 53C27
Keywords and phrases: Dirac equation, regularity, energy identity
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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.