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arXiv · 1809.07241

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

Juergen Jost·Lei Liu·Miaomiao Zhu
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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.

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Juergen Jost, Lei Liu, Miaomiao Zhu. 2018-09-19. Energy identity for a class of approximate Dirac-harmonic maps from surfaces with boundary. https://arxiv.org/abs/1809.07241

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