论文标题
带有PIC1的歧管弯曲曲率
Manifolds with PIC1 pinched curvature
论文作者
论文摘要
最近，已证明（Lee-Top 2022，Deruelle-Schulze-Simon 2022，Lott 2019），三维完整的歧管，具有非固定的RICCI曲率必须是平坦的或紧凑的，从而确认了汉密尔顿的猜想。在本文中，我们将工作概括为从非紧凑型捏夹的三个序列的RICCI流动，以证明具有较高维度的类似物。我们一直以任意完整的非紧凑型歧管开始，构建了RICCI流动的解决方案。作为一种应用，我们证明，pic1的非阴性复合部分曲率的任何完整歧管都必须是平坦的或紧凑的。
Recently it has been proved (Lee-Topping 2022, Deruelle-Schulze-Simon 2022, Lott 2019) that three-dimensional complete manifolds with non-negatively pinched Ricci curvature must be flat or compact, thus confirming a conjecture of Hamilton. In this paper we generalise our work on the existence of Ricci flows from non-compact pinched three-manifolds in order to prove a higher-dimensional analogue. We construct a solution to Ricci flow, for all time, starting with an arbitrary complete non-compact manifold that is PIC1 pinched. As an application we prove that any complete manifold of non-negative complex sectional curvature that is PIC1 pinched must be flat or compact.
