Limiting Behavior of the Ricci Flow

这一建议旨在获得关于收敛Ricci流和Kahler Ricci流的信息，并了解可能得到的唯一极限度量的结构。这一建议还涉及到流的极限和收敛速度的唯一性。在一个极限度量下，收敛的Ricci流在可积性假设下的极限的唯一性被主要研究者在她的论文中考虑。主要研究人员建议在没有可积性假设的情况下研究唯一性问题。一般而言，给出的程序处理流形上的一些非线性偏微分方程组。尽管这个问题听起来非常几何，但它与来自PDE的估计和技术密切相关。在这个提案中，这两种方法结合在一起，PI将探索如何理解流动的极限和描述可能发生的奇点的问题。

This proposal aims to obtaining information about converging Ricci and Kahler Ricci flows and understanding the structure of possibly singular limit metrics one gets. This proposal is also concerned about the uniqueness of a limit and a rate of convergence of the flow. The uniqueness of a limit of the converging Ricci flows under the integrability assumption on one of the limit metrics has been considered by the principal investigator in her dissertation. The principal investigator proposes to study the uniqueness question in the absence of the integrability assumption.Broadly speaking the given program deals with some nonlinear partial differential equations on manifolds. Though the problem sounds very geometric, it is tightly related to the estimates and techniques that come from PDEs. In this proposal these two methods come together and the PI will explore the question of how to understand the limit of the flow and describe the singularities that can occur.