On the evolution of regularized Dirac-harmonic Maps from closed surfaces

Abstract

We study the evolution equations for a regularized version of Dirac-harmonic maps from closed Riemannian surfaces. We establish the existence of a global weak solution for the regularized problem, which is smooth away from finitely many singularities. Moreover, we discuss the convergence of the evolution equations and address the question if we can remove the regularization in the end.

References in corpus (11)

• Dirac-harmonic maps from index theory
• Liouville Theorems for Dirac-Harmonic Maps
• Some explicit constructions of Dirac-harmonic maps
• Some aspects of Dirac-harmonic maps with curvature term
• Dirac-harmonic maps with torsion
• Magnetic Dirac-harmonic maps
• Energy estimates for the supersymmetric nonlinear sigma model and applications
• The evolution equations for regularized Dirac-geodesics
• A vanishing result for the supersymmetric nonlinear sigma model in higher dimensions
• Global existence of Dirac-wave maps with curvature term on expanding spacetimes
• Energy methods for Dirac-type equations in two-dimensional Minkowski space

Cited by in corpus (2)

• Minimal $W^{s,\frac{n}{s}}$-harmonic maps in homotopy classes
• Estimates for solutions of Dirac equations and an application to a geometric elliptic-parabolic problem