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

Min Chun Hong, Gang Tian, Hao Yin

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

In this paper we introduce an α-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-flow with smooth initial value. We prove that the limit of the solutions of the α-flow as α → 1 is a weak solution to the Yang-Mills flow. By an application of the α-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].

Original languageEnglish (US)
Pages (from-to)75-120
Number of pages46
JournalCommentarii Mathematici Helvetici
Volume90
Issue number1
DOIs
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Sacks-Uhlenbeck functional
  • Yang-Mills flow

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