Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

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:
Apr 29, 2015
Published:
Apr 30, 2015
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