论文标题
perelman-type无呼吸定理，用于非政策ricci流
Perelman-type no breather theorem for noncompact Ricci flows
论文作者
论文摘要
在本文中，我们首先表明，从下方界定的Ricci曲率的完全收缩的呼吸器必须是缩小的梯度Ricci Soliton。该结果有多个应用程序。首先，我们可以将所有完整的$ 3 $维度分类归类。其次，我们可以证明，每个完全缩小的Ricci soliton都具有从下面界定的RICCI曲率，必须是梯度 - Naber结果的概括。此外，我们为渐近缩小的梯度Ricci Soliton的存在发展了一般条件，希望这将有助于对古代解决方案的研究。
In this paper, we first show that a complete shrinking breather with Ricci curvature bounded from below must be a shrinking gradient Ricci soliton. This result has several applications. First, we can classify all complete $3$-dimensional shrinking breathers. Second, we can show that every complete shrinking Ricci soliton with Ricci curvature bounded from below must be gradient -- a generalization of Naber's result. Furthermore, we develop a general condition for the existence of the asymptotic shrinking gradient Ricci soliton, which hopefully will contribute to the study of ancient solutions.
