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MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

Received:
Mar 27, 2017
Published:
Mar 27, 2017
Keywords:
Supersymmetric nonlinear sigma model, Dirac-harmonic maps with $\lambda-$curvature term, Monotonicity formula, partial regularity

Related publications

inJournal
2019 Journal Open Access
Jürgen Jost, Lei Liu and Miaomiao Zhu

Regularity of Dirac-harmonic maps with \(\lambda\)-curvature term in higher dimensions

In: Calculus of variations and partial differential equations, 58 (2019) 6, p. 187