论文标题
RICCI流的非收获极限的结构理论
Structure theory of non-collapsed limits of Ricci flows
论文作者
论文摘要
在本文中，我们表征了Ricci流的非汇总限制。我们表明，这种限制在抛物线意义上远离一组condimension $ \ geq 4 $，并且每个点的切线流是通过梯度缩小孤子来给出的，可能带有一组奇异的codimension $ \ geq 4 $。此外，我们获得了具有最佳尺寸边界的单数集的分层结果，这取决于切线流的对称性。我们的方法还暗示了相应的定量分层结果和预期的$ l^p $ - 外观边界。 作为我们理论的应用，我们获得了Ricci流动在第一个奇异时间的奇异性形成的描述，以及表征不朽流动的长期行为的厚实的分解。这些结果将Perelman的结果推广到较高的维度。我们还获得了伪cenerem的后退定理，并讨论了其他几个应用程序。
In this paper we characterize non-collapsed limits of Ricci flows. We show that such limits are smooth away from a set of codimension $\geq 4$ in the parabolic sense and that the tangent flows at every point are given by gradient shrinking solitons, possibly with a singular set of codimension $\geq 4$. We furthermore obtain a stratification result of the singular set with optimal dimensional bounds, which depend on the symmetries of the tangent flows. Our methods also imply the corresponding quantitative stratification result and the expected $L^p$-curvature bounds. As an application of our theory, we obtain a description of the singularity formation of a Ricci flow at its first singular time and a thick-thin decomposition characterizing the long-time behavior of immortal flows. These results generalize Perelman's results in dimension 3 to higher dimensions. We also obtain a Backwards Pseudolocality Theorem and discuss several other applications.
