Variational Problems in Differential Geometry

在本研究中，我们研究了紧致四维流形上Yang-Mills热流解的一个性质。我们得到了一类“小数据整体存在性”的结果，紧4-流形上光滑联络的能量存在下界。该界由原丛的拓扑不变量决定。在本研究中，我们证明了，如果初始数据的能量是接近的界限，那么存在一个时间整体光滑解的杨米尔斯热流。

In this research, we study a behavior of solutions of Yang-Mills heat flow on compact 4-manifolds. We obtain result which is a type of "small data global existence".It is well-known that there exists the lower bound of the energy of smooth connections over compact 4-manifolds. The bound is determined by the topological invariant of the pricipal bundle. In this research, we prove that if the energy of the initial data is close to the bound, then there exists a time-global smooth solution of the Yang-Mills heat flow.