Entropy, Stability, and Yang-Mills flow
Entropy, Stability, and Yang-Mills flow
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DOI：
10.1142/s0219199715500327
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发表时间：
2014-10
期刊：
影响因子：
--
通讯作者：
C. Kelleher;J. Streets
中科院分区：
文献类型：
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作者：
C. Kelleher;J. Streets
在Colding-Minicozzi工作的基础上，我们定义了$\mathbb R^n$上以收缩的Yang-Mills孤子为临界点的连通的熵的概念.与Colding-Minicozzi一样，这个熵是隐式定义的，很难分析。我们证明了一个定理的熵稳定性的某些线性算子的谱与孤立子。这进一步导致孤子的间隙定理。这些结果指向一个更广泛的战略研究“通用奇点”的杨米尔斯流，我们讨论了这种战略的差异，在尺寸$n=4$与$n \geq 5$。
Following work of Colding-Minicozzi, we define a notion of entropy for connections over $\mathbb R^n$ which has shrinking Yang-Mills solitons as critical points. As in Colding-Minicozzi, this entropy is defined implicitly, making it difficult to work with analytically. We prove a theorem characterizing entropy stability in terms of the spectrum of a certain linear operator associated to the soliton. This leads furthermore to a gap theorem for solitons. These results point to a broader strategy of studying "generic singularities" of Yang-Mills flow, and we discuss the differences in this strategy in dimension $n=4$ versus $n \geq 5$.