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.

这一建议旨在获得关于收敛Ricci流和Kahler Ricci流的信息，并理解可能得到的奇异极限度量的结构。该建议还关注了流的极限和收敛速度的唯一性。本文主要研究了收敛Ricci流在极限指标可积性假设下极限的唯一性。作者提出在没有可积性假设的情况下研究唯一性问题。一般来说，给出的程序处理流形上的一些非线性偏微分方程。虽然这个问题听起来很几何，但它与来自pde的估计和技术密切相关。在这个提议中，这两种方法结合在一起，PI将探索如何理解流的极限和描述可能发生的奇点的问题。