论文标题
新的高级阳阳 - 米尔斯 - 里曼尼亚人流动$ 4 $ - manifold
A new higher order Yang--Mills--Higgs flow in Riemannian $4$-manifold
论文作者
论文摘要
令$（m，g）$为封闭的Riemannian $ 4 $ - manifold，让$ e $是$ m $的矢量捆绑包，结构组$ g $，其中$ g $是一个紧凑的谎言组。在本文中，我们考虑了一个新的高阶杨 - 米尔斯 - higgs功能，其中希格斯字段是$ω^0（\ textmd {ad} e）$的部分。我们表明，在适当的条件下，梯度流的解决方案不会达到任何有限的时间奇点。如果$ e $是线条捆绑包，我们可以使用不同的爆破过程，并在\ cite {z1}中获得长期结果的改进。该证明与绿色函数的属性相当相关，绿色功能与\ cite {ke，sa，z1}中的先前技术有很大不同。
Let $(M,g)$ be a closed Riemannian $4$-manifold and let $E$ be a vector bundle over $M$ with structure group $G$, where $G$ is a compact Lie group. In this paper, we consider a new higher order Yang--Mills--Higgs functional, in which the Higgs field is a section of $Ω^0(\textmd{ad}E)$. We show that, under suitable conditions, solutions to the gradient flow do not hit any finite time singularities. In the case that $E$ is a line bundle, we are able to use a different blow up procedure and obtain an improvement of the long time result in \cite{Z1}. The proof is rather relevant to the properties of the Green function, which is very different from the previous techniques in \cite{Ke,Sa,Z1}.
