Precise asymptotics of the Ricci flow neckpinch
Precise asymptotics of the Ricci flow neckpinch
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DOI：
10.4310/cag.2007.v15.n4.a6
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发表时间：
2005-11
影响因子：
0.7
通讯作者：
S. Angenent;Dan Knopf
中科院分区：
文献类型：
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作者：
S. Angenent;Dan Knopf
1.1.来路。在几乎所有已知的里奇流应用中，充分了解奇点形成是很有价值的。试探一下，至少有三个原因。第一个是人们期望有限时间奇点能够针对广泛的初始数据形成。事实上，如果标量曲率严格为正，这种奇点是不可避免的。第二个原因是，人们期望解的几何形状类似于正在发展的奇点的时空邻域中的标准模型（例如，自相似解）。第三个原因是，对正在发展的奇点有足够详细的了解有助于进行几何拓扑手术，通过几何拓扑手术，里奇流可以分解给定的流形。
1.1. Antecedents. In virtually all known applications of the Ricci flow, it is valuable to have a good understanding of singularity formation. Heuristically, there are at least three reasons for this. The first is that one expects finite-time singularities to form for a broad spectrum of initial data. Indeed, such singularities are inevitable if the scalar curvature is strictly positive. The second reason is that one expects the geometry of a solution to resemble a standard model (for example, a self-similar solution) in a space-time neighborhood of a developing singularity. The third reason is that having a sufficiently detailed picture of a developing singularity facilitates the geometric-topological surgeries by which Ricci flow decomposes a given manifold.