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

Open Access


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

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.


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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanPeople’s Republic of China
  2. 2.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  3. 3.Department of Mathematics and Computer ScienceUniversity of LeipzigLeipzigGermany
  4. 4.Institute of MathematicsUniversity FreiburgFreibrugGermany

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