The maximum principle and the Dirichlet problem for Dirac-harmonic maps
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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.
KeywordsDirac-harmonic map Maximum principle Uniqueness Existence
Mathematics Subject ClassificationPrimary 58E20 Secondary 53C27
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement no. 267087. The research of QC is also partially supported by NSFC and RFDP of China. The authors thank the Max Planck Institute for Mathematics in the Sciences for good working conditions when this work was carried out.
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