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

Jürgen Jost, Lei Liu, and Miaomiao Zhu

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Submission date: 30. Jan. 2017 (revised version: June 2017)
Pages: 28
published in: Annales de l'Institut Henri Poincaré / C, 36 (2019) 2, p. 365-387 
DOI number (of the published article): 10.1016/j.anihpc.2018.05.006
Bibtex
MSC-Numbers: 53C43, 58E20
Keywords and phrases: Dirac-harmonic maps, approximate Dirac-harmonic maps, Dirac-harmonic map ow, energy identity, boundary blow-up
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Abstract:
For a sequence of coupled fields {(ϕ_n,ψ_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