Mathematical Sciences: Deformations of Complex Structures

数学科学：复杂结构的变形

• 批准号: 9500557
• 负责人: Bernard Maskit
• 金额: $ 40.5万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500557&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Deformations; Complex; Structures

9500557 Maskit This project is concerned with several different aspects of complex analysis and function theory: moduli of Riemann surfaces via Eichler cohomology of Kleinian groups, the Schottky problem, geometric formulation of 2-dimensional quantum gravity, and Hausdorff dimension and the boundary behavior of conformal mappings are among the topics proposed. Function theory is the study of functions of one independent complex variable, and has a classical origin. A notable aspect of function theory is the use of Riemann surfaces; given a locally defined complex function one associates an abstract (multi-sheeted) surface, called the Riemann surface of the function, via analytic continuation. This Riemann surface carries all the essential information about the original function and its possible regular extensions. The proposed project has to do with classifying and understanding the totality of such Riemann surfaces.

9500557 Maskit这个项目涉及复分析和泛函理论的几个不同方面：通过Kleinan群的Eichler上同调的Riemann曲面的模，肖特基问题，二维量子引力的几何公式，以及Hausdorff维度和共形映射的边界行为是提出的主题之一。函数论研究的是一个独立的复变量的函数，它有着经典的起源。函数论的一个值得注意的方面是黎曼曲面的使用；给定一个局部定义的复杂函数，人们通过解析延拓将抽象的(多层)曲面联系在一起，称为函数的黎曼曲面。这个黎曼曲面包含了关于原始函数及其可能的正则扩张的所有基本信息。拟议的项目涉及对这种黎曼曲面的整体进行分类和理解。