JournalscmhVol. 90, No. 1pp. 75–120

The Yang–Mills α\alpha-flow in vector bundles over four manifolds and its applications

  • Min-Chun Hong

    The University of Queensland, Brisbane, Australia
  • Gang Tian

    Princeton University, USA
  • Hao Yin

    University of Science and Technology of China, Hefei, China
The Yang–Mills $\alpha$-flow in vector bundles over four manifolds and its applications cover
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Abstract

In this paper we introduce an α\alpha-flow for the Yang-Mills functional in vector bundles over four dimensional Riemannian manifolds, and establish global existence of a unique smooth solution to the α\alpha-flow with smooth initial value. We prove that the limit of the solutions of the α\alpha-flow as α1\alpha\to 1 is a weak solution to the Yang-Mills flow. By an application of the α\alpha-flow, we then follow the idea of Sacks and Uhlenbeck [22] to prove some existence results for Yang-Mills connections and improve the minimizing result of the Yang-Mills functional of Sedlacek [26]

Cite this article

Min-Chun Hong, Gang Tian, Hao Yin, The Yang–Mills α\alpha-flow in vector bundles over four manifolds and its applications. Comment. Math. Helv. 90 (2015), no. 1, pp. 75–120

DOI 10.4171/CMH/347