Linear and Nonlinear Analysis on Complete Kahler Manifolds

完全卡勒流形的线性和非线性分析

• 批准号: 0328624
• 负责人: Lei Ni
• 金额: $ 5.87万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-09-01 至 2005-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0328624&HistoricalAwards=false
• 关键词: Linear; Nonlinear; Analysis; Complete; Kahler

ABSTRACT DMS - 0203023.PI: Lei NiThe principle investigator proposes to study the interplay between thegeometry and the analysis on complete Kaehler manifolds. The focus will belinear and nonlinear analysis on such manifolds. The main tool is solvingthe linear equation, such as the Poisson equation and Poincare-Lelongequation, and the nonlinear equations such as the Kaehle-Ricci flow. Thegoal is to understand the space of holomorphic functions (plurisubharmonicfunctions), the interplay between the geometry and the function theory andapplying the results to the uniformization of complete Kaehler manifoldswith nonnegative curvature.The manifold is the space where every physical event happens. Theglobal analysis on manifolds studies the overall properties of themanifolds by piecing together the local information. Kaehler manifolds arethe basic block in the universe model according to the string theory. The proposed studyhas close connection with the theory of general relativity and stringtheory. The nonlinear differential equations studied in the proposal haveapplications in the study of the structure of complicated molecules,liquid-gas boundary, and even the large scale networks.

摘要DMS -0203023.PI：Lei Nithe原则研究者建议研究地几何与完整Kaehler歧管的分析之间的相互作用。重点将在此类流形上进行双线性和非线性分析。主要工具是求解线性方程，例如Poisson方程和繁殖性 - 烯词，以及非线性方程，例如Kaehle-Ricci流。目标是了解全态函数的空间（PlurisubharmonicFunctions），几何形状与函数理论之间的相互作用，并将结果应用于完整的Kaehler歧管非分泌曲率的均匀化。流形的歧管是每个事件发生的空间。对流形的全球分析通过将局部信息拼凑在一起研究theAnifolds的整体特性。 Kaehler根据字符串理论将宇宙模型中的基本块流动。拟议的研究与一般相对论和弦理论的理论紧密联系。在提案中研究的非线性微分方程在研究复杂分子，液态气边界甚至大规模网络的结构的研究中。