Dirac-geodesics and their heat flows

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• 作者：Qun Chen ; Jürgen Jost ; Linlin Sun…
• 关键词：58E10 ; 58J35 ; 53C22 ; 53C27
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：54
• 期：3
• 页码：2615-2635
• 全文大小：510 KB
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• 作者单位：Qun Chen (1)
  Jürgen Jost (2)
  Linlin Sun (1) (2)
  Miaomiao Zhu (2)
  
  1. School of Mathematics and Statistics, Wuhan University, Hubei, 430072, China
  2. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103, Leipzig, Germany
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Systems Theory and Control
  Calculus of Variations and Optimal Control
  Mathematical and Computational Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0835

文摘

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). Mathematics Subject Classification 58E10 58J35 53C22 53C27