Limiting Behavior of the Ricci Flow

里奇流的限制行为

• 批准号: 0604657
• 负责人: Natasa Sesum
• 金额: $ 9.62万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604657&HistoricalAwards=false
• 关键词: Limiting; Behavior; Ricci; Flow

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.

该建议旨在获取有关融合Ricci和Kahler Ricci流动的信息，并了解一个可能的奇异极限指标的结构。该建议还关注限制的独特性和流量收敛速度。首席研究者在论文中考虑了限制ricci流动在一个极限指标之一下流动的限制的唯一性。首席研究者建议在没有整合性假设的情况下研究唯一性问题。在路线上，给定的程序涉及流形的一些非线性偏微分方程。尽管问题听起来很几何，但它与来自PDE的估计和技术密切相关。在此提案中，这两种方法聚集在一起，PI将探讨如何理解流动限制并描述可能发生的奇点的问题。