论文标题
带有任意初始度量的边界上的歧管上的RICCI流动
Ricci Flow on Manifolds with Boundary with Arbitrary Initial Metric
论文作者
论文摘要
在本文中，我们研究了具有边界的歧管上的RICCI流动。在本文的第一部分中，我们证明了解决方案的短期存在和独特性，其中边界在积极的时间内立即变得脐带。在本文的第二部分中，我们证明我们在第一部分中构建的流量保留了自然边界条件。更具体地说，如果初始度量标准具有凸边界，则该流量可以保留正曲率算子和PIC1，PIC2条件。此外，如果初始度量标准具有两键边界，则该流量保留了PIC条件。
In this paper, we study the Ricci flow on manifolds with boundary. In the first part of the paper, we prove short-time existence and uniqueness of the solution, in which the boundary becomes instantaneously umbilic for positive time. In the second part of the paper, we prove that the flow we constructed in the first part preserves natural boundary conditions. More specifically, if the initial metric has a convex boundary, then the flow preserves positive curvature operator and the PIC1, PIC2 conditions. Moreover, if the initial metric has a two-convex boundary, then the flow preserves the PIC condition.
