Calculus of Variations and Partial Differential Equations

, Volume 47, Issue 1, pp 87-116

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

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

  • Qun ChenAffiliated withSchool of Mathematics and Statistics, Wuhan UniversityMax Planck Institute for Mathematics in the Sciences
  • , Jürgen JostAffiliated withMax Planck Institute for Mathematics in the SciencesDepartment of Mathematics and Computer Science, University of Leipzig Email author 
  • , Guofang WangAffiliated withInstitute of Mathematics, University Freiburg


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