2021/12/22 by Wang Guan Xiang, Xiang, Wang Guan, Zhang Chuan Jing +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2112.11703
openalex publication_date 2021/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we shall prove that, on a non-flat Riemannian vector bundle over a compact Riemannian manifold, the smooth solution of the Yang-Mills flow will blow up in finite time if the energy of the initial connection is small enough. We also consider the finite time blow up for the Yang-Mills flow with the initial curvature near the harmonic form. Furthermore, when E is a holomorphic vector bundle over a compact Kähler manifold, then E will admit a projective flat structure if the trace free part of Chern curvature is small enough.