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MiS Preprint
25/2017
Regularity of Dirac-harmonic maps with $\lambda-$curvature term in higher dimensions
Jürgen Jost, Lei Liu and Miaomiao Zhu
Abstract
In this paper, we will study the partial regularity for stationary Dirac-harmonic maps with $\lambda-$curvature term. For a weakly stationary Dirac-harmonic map with $\lambda-$curvature term $(\phi,\psi)$ from a smooth bounded open domain $\Omega\subset\mathbb{R}^m$ with $m\geq2$ to a compact Riemannian manifold $N$, if $\psi\in W^{1,p}(\Omega)$ for some $p>\frac{2m}{3}$, we prove that $(\phi, \psi)$ is smooth outside a closed singular set whose $(m-2)$-dimensional Hausdorff measure is zero. Furthermore, if the target manifold $N$ does not admit any harmonic sphere $S^l$, $l=2,...,m-1$, then $(\phi,\psi)$ is smooth.