Complex Analysis

复杂分析

• 批准号: 9704837
• 负责人: David Barrett
• 金额: $ 7.5万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-06-01 至 2001-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704837&HistoricalAwards=false
• 关键词: Complex; Analysis

9704837 Barrett This project lies in the general area of several complex variables. Among the topics to be pursued are: function theory on the basins of superattracting fixed points of multivariate complex dynamical systems; graph-theoretic methods for analysis of problems on open Riemann surfaces; Seiberg-Witten metrics on Riemann surfaces; boundary behavior of biholomorphic maps in higher dimensions. Research in several complex variables deals with spaces modeled on complex Euclidean space and mappings between them. Complex numbers, originally introduced in the study of polynomial functions, continue to be useful in simplifying and unifying various aspects of more general functions and maps. Moreover, it has found applications in other parts of mathematics and other sciences such as dynamical systems and theoretical physics.

小行星9704837 该项目属于多复变量的一般领域。其中要追求的主题是：功能理论的盆地超吸引不动点的多元复杂的动力系统;图论方法分析问题的开放黎曼曲面;塞伯格-威滕度量黎曼曲面;边界行为的双全纯映射在更高的维度。 多复变量的研究涉及以复欧几里得空间为模型的空间以及它们之间的映射。复数最初是在多项式函数的研究中引入的，现在仍然可以用于简化和统一更一般的函数和映射的各个方面。此外，它还在数学的其他部分和其他科学，如动力系统和理论物理学中得到应用。