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MiS Preprint

Dirac-geodesics and their heat flows

Qun Chen, Jürgen Jost, Linlin Sun and Miaomiao Zhu


Dirac-geodesics are Dirac-harmonic maps from one dimensional domains. In this paper, we introduce the heat flow for Dirac-geodesics and establish its long-time existence and an asymptotic property of the global solution. We classify Dirac-geodesics on the standard 2-sphere $S^2(1)$ and the hyperbolic plane $\mathbb{H}^2$, and derive existence results on topological spheres and hyperbolic surfaces. These solutions constitute new examples of coupled Dirac-harmonic maps (in the sense that the map part is not simply a harmonic map).

Apr 29, 2015
Apr 30, 2015
MSC Codes:
58E10, 58J35, 53C22, 53C27
Dirac-geodesics, heat flow

Related publications

2015 Repository Open Access
Qun Chen, Jürgen Jost, Linlin Sun and Miaomiao Zhu

Dirac-geodesics and their heat flows

In: Calculus of variations and partial differential equations, 54 (2015) 3, pp. 2615-2635