Time Zero Regularity of Ricci Flow
Time Zero Regularity of Ricci Flow
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DOI：
10.1093/imrn/rnac300
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发表时间：
2022-02
影响因子：
1
通讯作者：
Man-Chun Lee;P. Topping
中科院分区：
文献类型：
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作者：
Man-Chun Lee;P. Topping
我们考虑的问题，当一个光滑的Ricci流，为积极的时间，达到光滑的初始数据在弱意义下必须光滑到初始时间。我们获得了一个例子的曲率估计，其中这失败了[26]中给出的。我们证明了一个积极的结果的情况下，流满足下${\ensuremath {K}_{\textrm {IC}_1}$曲率界，相当于一个较低的Ricci界在三维。作为应用，我们证明了WPIC 1流形的Gromov-Hausdorff极限是WPIC 1.
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 that was given in [26]. We prove a positive result in the case that the flow satisfies a lower ${\ensuremath {\textrm {K}_{\textrm {IC}_1}}}$ 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.