Geodesic
Energy identity for a class of approximate Dirac-harmonic maps from surfaces with boundary
Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 2, pp. 365-387

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For a sequence of coupled fields {(ϕn,ψn)} 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.

DOI : 10.1016/j.anihpc.2018.05.006
Classification : 53C43, 58E20
Keywords: Dirac-harmonic maps, Approximate Dirac-harmonic maps, Dirac-harmonic map flow, Energy identity, Boundary blow-up 
@article{AIHPC_2019__36_2_365_0,
     author = {Jost, J\"urgen and Liu, Lei and Zhu, Miaomiao},
     title = {Energy identity for a class of approximate {Dirac-harmonic} maps from surfaces with boundary},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {365--387},
     publisher = {Elsevier},
     volume = {36},
     number = {2},
     year = {2019},
     doi = {10.1016/j.anihpc.2018.05.006},
     mrnumber = {3913190},
     zbl = {1416.53060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2018.05.006/}
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Jost, Jürgen; Liu, Lei; Zhu, Miaomiao. Energy identity for a class of approximate Dirac-harmonic maps from surfaces with boundary. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 2, pp. 365-387. doi: 10.1016/j.anihpc.2018.05.006

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