Regularity of minimizing harmonic maps into the sphere.

Richard Schoen; Karen Uhlenbeck

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The boundary value problem for Dirac-harmonic maps

Qun Chen, Jürgen Jost, Guofang Wang, Miaomiao Zhu (2013)

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Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian...

$f$ -harmonic maps which map the boundary of the domain to one point in the target.

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