中国科学技术大学学报 ›› 2016, Vol. 46 ›› Issue (8): 629-635.DOI: 10.3969/j.issn.0253-2778.2016.08.002

• 论著 • 上一篇    

关于杨-米尔斯联络的一些能量性质

施继旭   

  1. 中国科学技术大学数学科学学院,安徽合肥 230026
  • 收稿日期:2015-12-07 修回日期:2016-05-22 接受日期:2016-05-22 出版日期:2016-05-22 发布日期:2016-05-22

Some energy properties of Yang-Mills connections

SHI Jixu   

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
  • Received:2015-12-07 Revised:2016-05-22 Accepted:2016-05-22 Online:2016-05-22 Published:2016-05-22
  • About author:SHI Jixu, male, born in 1991, master. Research field: mathematical physics. E-mail: sjx1991@mail.ustc.edu.cn
  • Supported by:
    Supported by the Wu Wen-Tsun Key Laboratory of Mathematics at USTC of the Chinese Academy of Sciences.

摘要: M=Mn是一个紧致的黎曼流形,E是M上的向量丛,A是E上具有Ln[]2曲率的杨-米尔斯联络.通过证明一个关于|FA|n[]2的平均值不等式,得到了一列能量有限解具有能量集中的性质.还得到E是一个平坦丛,否则能量一定具有非零下界.

关键词: 杨-米尔斯联络, 能量集中, 能量间隙

Abstract: E is a vector bundle over a compact Riemannian manifold M=Mn, n≥4, and A is a Yang-Mills connection with Ln[]2 curvature FA on E. Through a mean value inequality of the density |FA|n[]2, an energy concentrate principle of sequences of solutions that have bounded energy is proved. Unless E is a flat bundle, the energy must be bounded from below by some positive constant.

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