Uniqueness and nonuniqueness for Ricci flow on surfaces: Reverse cusp singularities
Uniqueness and nonuniqueness for Ricci flow on surfaces: Reverse cusp singularities
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DOI：
10.1093/imrn/rnr082
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发表时间：
2010-10
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影响因子：
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通讯作者：
P. Topping
中科院分区：
文献类型：
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作者：
P. Topping
我们扩展的概念，它意味着一个完整的里奇流有一个给定的初始度量，并考虑由此产生的适定性问题，出现在二维的情况下。一方面，我们构造的例子表明，表面的尖点可以通过保持尖点或收缩它们演变的非唯一性。另一方面，通过对初始度量增加一个非连续性假设，我们建立了一个唯一性结果。
We extend the notion of what it means for a complete Ricci flow to have a given initial metric, and consider the resulting well-posedness issues that arise in the 2D case. On one hand we construct examples of nonuniqueness by showing that surfaces with cusps can evolve either by keeping the cusps or by contracting them. On the other hand, by adding a noncollapsedness assumption for the initial metric, we establish a uniqueness result.