Mathematical Sciences: Analysis in the Large

数学科学：大分析

• 批准号: 8704325
• 负责人: Isaac Chavel
• 金额: --
• 依托单位: CUNY City College
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-15 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8704325&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analysis; Large

Isaac Chavel and Edgar Feldman will continue their investigations of the effect of small perturbations of a manifold on the spectral and stochastic properties of the manifold. These investigations have progressed from studying the relation of eigenvalues of the Laplacian to the geometry and topology of the manifold to consideration of probabilistic formulations of these questions. The particular perturbations of the manifolds to be studied include adding long thin handles, deleting tubular neighborhoods of submanifolds or removing small domains. The investigators will also consider large time asymptotics of Brownian motion and heat diffusion.

艾萨克·查维尔和埃德加·费尔德曼将继续研究流形的小扰动对流形的谱和随机性质的影响。这些调查已经取得了进展，从研究拉普拉斯算子的特征值的几何和拓扑的流形考虑这些问题的概率公式。所研究的流形的特殊扰动包括添加细长柄、删除子流形的管状邻域或移除小区域。研究人员也将考虑布朗运动和热扩散的大时间渐近性。