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The maximum principle and the Dirichlet problem for Dirac-harmonic maps
Qun Chen, Jürgen Jost and Guofang Wang
We establish a maximum principle and uniqueness for Dirac-harmonic maps from a Riemannian spin manifold with boundary into a regular ball in any Riemannian manifold $N$. Then we prove an existence theorem for a boundary value problem for Dirac-harmonic maps.