平稳Yang-Mills联络在弱收敛下的非闭性
Nonclosure of stationary Yang-Mills connections under weak convergence
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中文总结 AI 辅助
本文构造了一列具有孤立奇点的平稳弱Yang-Mills联络，其弱极限非平稳，从而证明了平稳弱Yang-Mills联络在弱收敛下不封闭，并给出了调和映射中类似现象的Yang-Mills类比。
中文摘要 AI 辅助
我们在平凡向量丛$B^5\times\mathbb{R}^{15}$上构造了一列结构群为$\operatorname{SO}(15)$的平稳弱Yang-Mills联络，其弱极限是非平稳的弱Yang-Mills联络。受田刚关于Yang-Mills紧性研究中出现的平稳性问题启发，我们的结果确立了具有孤立奇点的平稳弱Yang-Mills联络弱闭性的失效。该结果也为丁伟、李骏和李驰关于调和映射所展示的现象提供了一个Yang-Mills类比。
英文摘要
We construct a sequence of stationary weak Yang-Mills connections on the trivial vector bundle $B^5\times\mathbb{R}^{15}$ with structure group $\operatorname{SO}(15)$ whose weak limit is a nonstationary weak Yang-Mills connection. Motivated by the stationarity question arising in Tian's work on Yang-Mills compactness, our result establishes the failure of weak closure for stationary weak Yang-Mills connections with an isolated singularity. It also provides a Yang-Mills analogue of the phenomenon exhibited by Ding, Li and Li for harmonic maps.
发表机构
- Tsinghua University（清华大学）
- Nanjing University（南京大学）
- Nanjing University of Science and Technology（南京理工大学）
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