AI 中文总结
本文研究非塌缩Ricci流极限空间的切流,证明负时间切片规则部分的测地凸性,并将其等同于度量完备化,从而与度量孤子对应。
AI 中文摘要
我们研究了Fang-Li意义下非塌缩Ricci流极限空间的切流。我们证明了每个负时间切片的规则部分是测地凸的:任何与规则部分相交的极小测地线,其整个内部都包含在该部分中。我们还把每个负时间切片等同于其规则黎曼部分的度量完备化,从而将负时间切流与其相关的度量孤子等同起来。
英文摘要
We study tangent flows of noncollapsed Ricci flow limit spaces in the sense of Fang-Li. We prove that the regular part of every negative time slice is geodesically convex: any minimizing geodesic that meets the regular part has its entire interior contained in it. We also identify each negative time slice with the metric completion of its regular Riemannian part, thereby identifying the negative-time tangent flow with its associated metric soliton.