Preprint 25/2017

Regularity of Dirac-harmonic maps with λcurvature term in higher dimensions

Jürgen Jost, Lei Liu, and Miaomiao Zhu

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Submission date: 27. Mar. 2017 (revised version: April 2017)
Pages: 25
published in: Calculus of variations and partial differential equations, 58 (2019) 6, art-no. 187 
DOI number (of the published article): 10.1007/s00526-019-1632-y
Keywords and phrases: Supersymmetric nonlinear sigma model, Dirac-harmonic maps with $\lambda-$curvature term, Monotonicity formula, partial regularity
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In this paper, we will study the partial regularity for stationary Dirac-harmonic maps with λcurvature term. For a weakly stationary Dirac-harmonic map with λcurvature term (ϕ,ψ) from a smooth bounded open domain Ω m with m 2 to a compact Riemannian manifold N, if ψ W1,p(Ω) for some p > 2m-  3, we prove that (ϕ,ψ) 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 Sl, l = 2,...,m 1, then (ϕ,ψ) is smooth.

24.11.2021, 02:19