Calculus of Variations and Partial Differential Equations

, Volume 47, Issue 1, pp 87–116

The maximum principle and the Dirichlet problem for Dirac-harmonic maps


  • Qun Chen
    • School of Mathematics and StatisticsWuhan University
    • Max Planck Institute for Mathematics in the Sciences
    • Max Planck Institute for Mathematics in the Sciences
    • Department of Mathematics and Computer ScienceUniversity of Leipzig
  • Guofang Wang
    • Institute of MathematicsUniversity Freiburg

DOI: 10.1007/s00526-012-0512-5


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.


Dirac-harmonic map Maximum principle Uniqueness Existence

Mathematics Subject Classification

Primary 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.

Open Access

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Copyright information

© The Author(s) 2012