论文标题
奇异性和差异性
Singularities and diffeomorphisms
论文作者
论文摘要
由于一组差异性，比较和识别指标可能非常困难。在不同的坐标中，两个指标甚至可能是相同的指标。这是量规问题。一般仪表问题非常微妙，尤其是对于非紧凑型空间。通常，如果人们使用特定情况的一些其他结构，则可以避免。但是，在许多问题中，没有其他结构。取而代之的是，我们直接以极大的一般性解决了量规问题。这些技术和想法适用于许多问题。我们使用它们来解决RICCI流动中众所周知的开放问题。我们通过解决PDE的非线性系统来解决量规问题。 PDE产生一种差异性，以片段定理的精神修复了适当的仪表，以进行小组行动。然后，我们显示出最佳的界限函数的最佳边界。
Comparing and recognizing metrics can be extraordinarily difficult because of the group of diffeomorphisms. Two metrics, that could even be the same, could look completely different in different coordinates. This is the gauge problem. The general gauge problem is extremely subtle, especially for non-compact spaces. Often it can be avoided if one uses some additional structure of the particular situation. However, in many problems there is no additional structure. Instead we solve the gauge problem directly in great generality. The techniques and ideas apply to many problems. We use them to solve a well-known open problem in Ricci flow. We solve the gauge problem by solving a nonlinear system of PDEs. The PDE produces a diffeomorphism that fixes an appropriate gauge in the spirit of the slice theorem for group actions. We then show optimal bounds for the displacement function of the diffeomorphism.
