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

Abstract

For a sequence of coupled fields $\{({\varphi }_n,{\psi }_n)\}$ 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.

to appear in Ann. Inst.H. Poincar Anal. Non Linaire https://doi.org/10.1016/j.anihpc.2018.05.006