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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
30/2015

Dirac-geodesics and their heat flows

Qun Chen, Jürgen Jost, Linlin Sun and Miaomiao Zhu

Abstract

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).

Received:
29.04.15
Published:
30.04.15
MSC Codes:
58E10, 58J35, 53C22, 53C27
Keywords:
Dirac-geodesics, heat flow

Related publications

inJournal
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