论文标题
三维RICCI流中的奇异模型
Singularity models in the three-dimensional Ricci flow
论文作者
论文摘要
RICCI流是给定歧管上Riemannian指标的自然进化方程。主要目标是了解奇异性形成。佩雷尔曼（Perelman）在2002年的壮观突破中获得了对尺寸奇异性形成的定性理解，$ 3 $。更确切地说，佩雷尔曼（Perelman）表明，RICCI流动中的每个有限时间奇异性$ 3 $都是以古老的$κ$ solution建模的。此外，佩雷尔曼（Perelman）证明了一个古代$κ$ solutions in Dimension $ 3 $的结构定理。 在这项调查中，我们讨论了最新的发展，这些事态发展导致了所有奇异模型的完整分类$ 3 $。此外，我们还提供了一个替代证明，以分类为$ 3 $的非策略稳定梯度Ricci Solitons（最初由作者在2012年证明）。
The Ricci flow is a natural evolution equation for Riemannian metrics on a given manifold. The main goal is to understand singularity formation. In his spectacular 2002 breakthrough, Perelman achieved a qualitative understanding of singularity formation in dimension $3$. More precisely, Perelman showed that every finite-time singularity to the Ricci flow in dimension $3$ is modeled on an ancient $κ$-solution. Moreover, Perelman proved a structure theorem for ancient $κ$-solutions in dimension $3$. In this survey, we discuss recent developments which have led to a complete classification of all the singularity models in dimension $3$. Moreover, we give an alternative proof of the classification of noncollapsed steady gradient Ricci solitons in dimension $3$ (originally proved by the author in 2012).
