Uniqueness and stability of Ricci flow through singularities
Uniqueness and stability of Ricci flow through singularities
复制标题
DOI：
10.4310/acta.2022.v228.n1.a1
复制
发表时间：
2017-09
期刊：
影响因子：
3.7
通讯作者：
R. Bamler;B. Kleiner
中科院分区：
文献类型：
--
作者：
R. Bamler;B. Kleiner
我们验证了Perelman的一个猜想，即存在一个从任意紧致黎曼3-流形出发的通过奇点的正则Ricci流。我们的主要结果是一个唯一性定理，这样的流量，其中，连同早先的存在定理的洛特和第二命名的作者，意味着佩雷尔曼的猜想。我们还表明，这种流动通过奇点连续依赖于它的初始条件，它可以得到作为一个限制的里奇流与手术。我们的结果有应用程序的研究的非同构群的三个流形-特别是广义Smale猜想-这将出现在随后的文件。
We verify a conjecture of Perelman, which states that there exists a canonical Ricci flow through singularities starting from an arbitrary compact Riemannian 3-manifold. Our main result is a uniqueness theorem for such flows, which, together with an earlier existence theorem of Lott and the second named author, implies Perelman's conjecture. We also show that this flow through singularities depends continuously on its initial condition and that it may be obtained as a limit of Ricci flows with surgery. Our results have applications to the study of diffeomorphism groups of three manifolds --- in particular to the Generalized Smale Conjecture --- which will appear in a subsequent paper.