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Regularity of Dirac-Harmonic Maps
International mathematics research notices
For any n-dimensional compact spin Riemannian manifold M with a given spin structure and a spinor bundle M, and any compact Riemannian manifold N, we show an -regularity theorem for weakly Dirac-harmonic maps (φ, ψ) : M ⊗ M → N ⊗ φ * T N. As a consequence, any weakly Dirac-harmonic map is proven to be smooth when n = 2. A weak convergence theorem for approximate Dirac-harmonic maps is established when n = 2. For n ≥ 3, we introduce the notation of stationary Dirac-harmonic maps and obtain adoi:10.1093/imrn/rnp064 fatcat:i35zyljt65chrfr7zws3koexna