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MiS Preprint

A global weak solution of the Dirac-harmonic map flow

Jürgen Jost, Lei Liu and Miaomiao Zhu


We show the existence of a global weak solution of the heat flow for Dirac-harmonic maps from compact Riemann surfaces with boundary when the energy of the initial map and the $L^2-$norm of the boundary values of the spinor are sufficiently small. The solution is unique and regular with the exception of at most finitely many singular times. We also discuss the behavior at the singularities of the flow.

As an application, we deduce some existence results for Dirac-harmonic maps.

Dirac-harmonic map, Dirac-harmonic flow, blow-up, Dirichlet boundary, chiral boundary, singularity

Related publications

2017 Repository Open Access
Jürgen Jost, Lei Liu and Miaomiao Zhu

A global weak solution of the Dirac-harmonic map flow

In: Annales de l'Institut Henri Poincaré / C, 34 (2017) 7, pp. 1851-1882