Mathematical Sciences: Differential Systems, Complex Analysis and Geometry

数学科学：微分系统、复分析和几何

• 批准号: 9625633
• 负责人: Masatake Kuranishi
• 金额: $ 15万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 2000-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9625633&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Differential; Systems; Complex

9625633 Kuranishi This project deals with a number of topics in several complex variables, exterior differential systems and differential geometry. In particular, the investigator plans to pursue the Cauchy-Riemann embedding problem, curvature prescription problems, the Radon transform on symmetric spaces and its application to isopectral rigidity, and kernels on weakly pseudoconvex domains and holomorphc extension problems. Many problems in differential geometry and complex analysis can be couched in the language of exterior differential systems - exterior differential systems are a generalization of systems of partial differential equations allowing them to be defined globally on curved spaces without having to introduce local coordinates. Several of the proposed problems deal with applications of exterior systems theory. The curvature prescription problem, in particular, seeks to find spaces satisfying a given set of curvature properties by solving an associated system of exterior equations on a smooth but otherwise bare space.

9625633仓西这个项目涉及几个复变量、外微分系统和微分几何中的许多主题。特别是，研究者计划研究Cauchy-Riemann嵌入问题，曲率规定问题，对称空间上的Radon变换及其在等谱刚性中的应用，以及弱伪凸域上的核和全纯扩张问题。微分几何和复杂分析中的许多问题都可以用外微分系统的语言来描述-外微分系统是偏微分方程组的推广，允许在弯曲空间上全局定义它们，而不必引入局部坐标。提出的几个问题涉及外部系统理论的应用。具体地说，曲率规定问题寻求通过在光滑的但不是空的空间上求解相关的外部方程组来寻找满足给定的曲率性质的空间。