Harmonic Forms and Topology of Complete Manifolds

完全流形的调和形式和拓扑

• 批准号: 0404817
• 负责人: Jiaping Wang
• 金额: $ 10.8万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0404817&HistoricalAwards=false
• 关键词: Harmonic; Forms; Topology; Complete; Manifolds

DMS-0404817P.I.: Jiaping Wang, University of Minnesota-Twin CitiesTitle: Harmonic forms and topology of complete manifoldsABSTRACTThis proposed project is about relating the analysis and topology on complete noncomapct manifolds. In particular, it is proposed to searchfor an extension of the de Rham-Hodge theory, and to relate the spectrum ofthe Hodge Laplacian to the topology of manifolds.The main objective of this project is to describe some large scalestructuresof objects which are high dimensional analogue of the unbounded surfaces.The approach is to inspect the physical steady states of a naturallydefinedenergy on such objects. The results and techniques are expected to beusefulin describing more complicated systems arising from physics, biology andotherbranches of science.

DMS-0404817 P.I.：王家平，明尼苏达大学双城分校题目：完备流形的调和形式与拓扑结构摘要本项目旨在将完备非完备流形的分析与拓扑结构联系起来。特别地，我们提出了寻求de Rham-Hodge理论的一个推广，并将Hodge Laplacian的谱与流形的拓扑联系起来.本项目的主要目标是描述一些类似于无界表面的高维物体的大尺度结构.方法是考察这些物体上自然定义的能量的物理稳定状态.这些结果和技术有望在描述物理学、生物学和其他科学分支中产生的更复杂的系统方面发挥作用。