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arXiv · 1705.08935

Short time existence of the heat flow for Dirac-harmonic maps on closed manifolds

Johannes Wittmann
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Abstract

The heat flow for Dirac-harmonic maps on Riemannian spin manifolds is a modification of the classical heat flow for harmonic maps by coupling it to a spinor. It was introduced by Chen, Jost, Sun, and Zhu as a tool to get a general existence program for Dirac-harmonic maps. For source manifolds with boundary they obtained short time existence and the existence of a global weak solution was established by Jost, Liu, and Zhu. We prove short time existence of the heat flow for Dirac-harmonic maps on closed manifolds.

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Johannes Wittmann. 2017-05-24. Short time existence of the heat flow for Dirac-harmonic maps on closed manifolds. https://arxiv.org/abs/1705.08935

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