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
Open AccessArticle

DOI: 10.1007/s00526-012-0512-5

Cite this article as:
Chen, Q., Jost, J. & Wang, G. Calc. Var. (2013) 47: 87. 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 mapMaximum principleUniquenessExistence

Mathematics Subject Classification

Primary 58E20Secondary 53C27
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© The Author(s) 2012