论文标题
旋转不变的Ricci流量的规范手术
Canonical surgeries in rotationally invariant Ricci flow
论文作者
论文摘要
我们在任何闭合的旋转不变的riemannian歧管上构建了通过手术的旋转不变的RICCI流动。我们证明，在[32]的意义上，一系列这种RICCI流动以手术为导向RICCI流动时空的序列。 Bamler-Kleiner [8]和Haslhofer [29]的结果保证了这些空间的独特性和稳定性给定初始数据。我们在环境中简化了此证明的各个方面，并表明对于旋转不变的RICCI流动，可以通过模棱两可的比较图来测量空间的接近度。最后，我们证明了这些RICCI流的奇异时间附近曲率的爆炸速率受剩余时间平方的倒数界定。
We construct a rotationally invariant Ricci flow through surgery starting at any closed rotationally invariant Riemannian manifold. We demonstrate that a sequence of such Ricci flows with surgery converges to a Ricci flow spacetime in the sense of [32]. Results of Bamler-Kleiner [8] and Haslhofer [29] then guarantee the uniqueness and stability of these spacetimes given initial data. We simplify aspects of this proof in our setting, and show that for rotationally invariant Ricci flows, the closeness of spacetimes can be measured by equivariant comparison maps. Finally we show that the blowup rate of the curvature near a singular time for these Ricci flows is bounded by the inverse of remaining time squared.
