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arXiv · 2112.11703

The finite time blow-up of the Yang-Mills flow

Wang Guan Xiang·Zhang Chuan Jing
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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 K\"ahler manifold, then $E$ will admit a projective flat structure if the trace free part of Chern curvature is small enough.

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Wang Guan Xiang, Zhang Chuan Jing. 2021-12-22. The finite time blow-up of the Yang-Mills flow. https://arxiv.org/abs/2112.11703

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