Mathematical Sciences: Differential Geometry, Partial Differential Equations and Several Complex Variables

数学科学：微分几何、偏微分方程和多个复变量

• 批准号: 9100715
• 负责人: Robert Greene
• 金额: $ 16.08万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9100715&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Differential; Geometry; Partial

The principal investigators will study problems in complex differential geometry and spectral geometry. Professor Greene will attempt to find biholomorphic invariants which can be used to classify domains with noncompact automorphism group. Professor Petersen will study the relationship between the topology and geometry of a manifold and the spectrum of the Laplace operator. The post doctoral associate supported by this award, S. Zhu, will study the relationship between topology and Ricci curvature. This award will support work in differential geometry which tries to relate global topological information to local analytic information. The local information generally is presented in the form of an invariant of a differential equation or system of equations. The information is then used to classify the domain or to obtain restrictions on the global "shape" of the set under consideration.

主要研究人员将研究复杂的问题 微分几何和谱几何。格林教授会 试图找到双全纯不变量，可用于 对具有非紧自同构群的域进行分类。教授 彼得森将研究拓扑结构之间的关系， 流形的几何和拉普拉斯算子的谱。 该奖项支持的博士后助理S。朱，威尔 研究拓扑与里奇曲率的关系。 该奖项将支持微分几何的工作， 尝试将全局拓扑信息与局部分析 信息.本地信息通常在 微分方程或系统的不变量的形式 方程然后使用该信息对域进行分类， 为了获得对集合的全局“形状”的限制， 考虑.