A global weak solution of the Dirac-harmonic map flow

Jürgen Jost, Lei Liu, and Miaomiao Zhu

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Submission date: 03. Jan. 2016 (revised version: March 2016)
Pages: 37
published in: Annales de l'Institut Henri Poincaré / C, 34 (2017) 7, p. 1851-1882 
DOI number (of the published article): 10.1016/j.anihpc.2017.01.002
Bibtex
Keywords and phrases: Dirac-harmonic map, Dirac-harmonic flow, blow-up, Dirichlet boundary, chiral boundary, singularity
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Abstract:
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 L²−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.