Limiting Behavior of the Ricci Flow

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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.