Mathematical Sciences: Riemannian Geometry and Geometric Complex Analysis

数学科学：黎曼几何和几何复分析

• 批准号: 9306956
• 负责人: Robert Greene
• 金额: $ 19.5万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9306956&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Riemannian; Geometry; Geometric

Riemannian Geometry and Geometric Complex Analysis Investigation is proposed in differential geometry, geometric several variables, and methods of partial differential equations in geometry, including the following specific topics: The Bergman metric geometry of pseudo-convex domains, compact manifolds of non-negative curvature, non-compact manifolds of non-negative curvature, the spectrum of the Laplacian, and the geometry of orbifolds. The overall research thrust of the project is the study of the relationship of the concept of curvature to the global geometry, topology, and analysis of Riemannian manifolds via geometric, complex analytic and partial differential equation methods.

黎曼几何和几何复分析是在微分几何、几何多变量和几何偏微分方程组的方法中提出的研究，包括以下具体主题：伪凸域的Bergman度量几何，非负曲率的紧致流形，非负曲率的非紧致流形，拉普拉斯的谱，以及奥布洛德的几何形状。该项目的总体研究重点是通过几何、复解析和偏微分方程式方法研究曲率概念与黎曼流形的整体几何、拓扑和分析的关系。