论文标题
RICCI流量的时间零规律性
Time zero regularity of Ricci flow
论文作者
论文摘要
我们考虑到平稳的RICCI流何时在积极的时间内获得平滑的初始数据，从而使弱意义上的平滑初始数据必须平滑至初始时间。我们获得了一个失败的示例的曲率估计。在流动满足较低的IC1曲率结合的情况下，我们证明了一个积极的结果，相当于在三个维度上结合的较低的RICCI。作为一种应用，我们证明WPIC1歧管的Gromov-Hausdorff限制为WPIC1。
We consider the problem of when a smooth Ricci flow, for positive time, that attains smooth initial data in a weak sense must be smooth down to the initial time. We obtain curvature estimates for an example where this fails. We prove a positive result in the case that the flow satisfies a lower IC1 curvature bound, equivalent to a lower Ricci bound in three dimensions. As an application, we prove that Gromov-Hausdorff limits of WPIC1 manifolds are WPIC1.
