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arXiv · 1303.0628

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

Min-Chun Hong·Gang Tian·Hao Yin
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Abstract

In this paper, we introduce an \alpha -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 \alpha -flow with smooth initial value. We prove that the limit of solutions of the \alpha -flow as \alpha\to 1 is a weak solution to the Yang-Mills flow. By an application of the \alpha -flow, we then follow the idea of Sacks and Uhlenbeck to prove some existence results for Yang-Mills connections and improve the minimizing result of the Yang-Mills functional of Sedlacek.

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Min-Chun Hong, Gang Tian, Hao Yin. 2013-03-04. The Yang-Mills \alpha -flow in vector bundles over four manifolds and its applications. https://arxiv.org/abs/1303.0628

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