2013/08/12 by Min-Chun Hong, Hong, Min-Chun, Lorenz Schabrun +1
Mathematics · #53C07 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.AP #math.DG #msc:53C07
paper · pdf · doi:10.48550/arxiv.1308.2704
25 pages (second version)
openalex publication_date 2013/08/12 · arxiv created 2014/02/18 · arxiv updated 2014/02/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We prove that the Yang-Mills α-functional satisfies the Palais-Smale condition. This guarantees the existence of critical points, which are called Yang-Mills α-connections. It was shown by Hong, Tian and Yin in [10] (to appear in Comm. Math. Helv.) that as α→ 1, a sequence of Yang-Mills α-connections converges to a Yang-Mills connection away from finitely many points. We prove an energy identity for such a sequence of Yang-Mills α-connections. As an application, we also prove an energy identity for the Yang-Mills flow at the maximal existence time.