JournalsaihpcVol. 36, No. 2pp. 365–387

Energy identity for a class of approximate Dirac-harmonic maps from surfaces with boundary

  • Jürgen Jost

    Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany, Department of Mathematics, Leipzig University, 04081 Leipzig, Germany
  • Lei Liu

    Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany
  • Miaomiao Zhu

    School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China
Energy identity for a class of approximate Dirac-harmonic maps from surfaces with boundary cover
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Abstract

For a sequence of coupled fields {(ϕn,ψn)}\{(\phi _{n},\psi _{n})\} from a compact Riemann surface M with smooth boundary to a general compact Riemannian manifold with uniformly bounded energy and satisfying the Dirac-harmonic system up to some uniformly controlled error terms, we show that the energy identity holds during a blow-up process near the boundary. As an application to the heat flow of Dirac-harmonic maps from surfaces with boundary, when such a flow blows up at infinite time, we obtain an energy identity.

Cite this article

Jürgen Jost, Lei Liu, Miaomiao Zhu, Energy identity for a class of approximate Dirac-harmonic maps from surfaces with boundary. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 2, pp. 365–387

DOI 10.1016/J.ANIHPC.2018.05.006