论文标题
在微弱的超级Ricci上流过领口
On Weak Super Ricci Flow through Neckpinch
论文作者
论文摘要
在本文中，我们研究了RICCI流动领口在度量测量空间的背景下。我们介绍了RICCI流量度量时空的概念以及与凸成本函数相关的弱（精致）超级RICCI流（成本函数增加了距离函数的凸功能）。我们对弱的超级RICCI流动的定义基于适当定义的最大扩散组件扩散的耦合收缩特性。 In our main theorem, we show that if a non-degenerate spherical neckpinch can be continued beyond the singular time by a smooth forward evolution then the corresponding Ricci flow metric measure spacetime through the singularity is a weak super Ricci flow for a (and therefore for all) convex cost functions if and only if the single point pinching phenomenon holds at singular times;即，如果形式的有限数量$ \ {x \} \ times \ sphere^n $在有限数量上形成奇点。我们还显示时空是精致的弱超级RICCI流动，并且仅当流量是平滑的RICCI流动，可能是最终的最终时间。
In this article, we study the Ricci flow neckpinch in the context of metric measure spaces. We introduce the notion of a Ricci flow metric measure spacetime and of a weak (refined) super Ricci flow associated to convex cost functions (cost functions which are increasing convex functions of the distance function). Our definition of a weak super Ricci flow is based on the coupled contraction property for suitably defined diffusions on maximal diffusion components. In our main theorem, we show that if a non-degenerate spherical neckpinch can be continued beyond the singular time by a smooth forward evolution then the corresponding Ricci flow metric measure spacetime through the singularity is a weak super Ricci flow for a (and therefore for all) convex cost functions if and only if the single point pinching phenomenon holds at singular times; i.e., if singularities form on a finite number of totally geodesic hypersurfaces of the form $\{x\} \times \sphere^n$. We also show the spacetime is a refined weak super Ricci flow if and only if the flow is a smooth Ricci flow with possibly singular final time.
