The Finite Time Blow-up of the Yang-Mills Flow

Abstract

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, E will admit a projectively flat structure if the trace-free part of Chern curvature is small enough.

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School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature