Direct minimizing method for Yang–Mills energy over SO(3) bundle
Direct minimizing method for Yang–Mills energy over SO(3) bundle
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DOI：
10.1007/s00208-023-02773-w
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发表时间：
2021-09
影响因子：
1.4
通讯作者：
Hao Yin
中科院分区：
文献类型：
--
作者：
Hao Yin
本文改进了结构群isSO(3)时闭合四流形上的Yang-Mills能量直接最小化法的已知结果。通过构造检验连接，证明了在一定的假设条件下，最小化序列强收敛于最小化序列。作为推论，存在Yang-Mills能量的最小值，它不是瞬子和阿贝尔连接的直接和。这为Stern （J Differ Geom 86(1): 163-188, 2010）的一个问题提供了一个否定的答案。
In this paper, we improve the known results on the direct minimizing method for Yang–Mills energy over closed four manifolds when the structure group isSO(3). By constructing test connections, we prove that some minimizing sequence converges strongly to a minimizer under certain assumptions. As a corollary, there exists an energy minimizer of the Yang–Mills energy, which is not a direct sum of instantons and abelian connections. This provides a negative answer to a question of Stern (J Differ Geom 86(1):163–188, 2010).