Mathematical Sciences: Research in Complex Analysis

数学科学：复分析研究

• 批准号: 9103585
• 负责人: Eric Bedford
• 金额: $ 11.7万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-03-15 至 1994-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103585&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Complex; Analysis

The principal investigator will continue his study of questions involving functions of several complex variables related to potential theory, dynamical systems and holomorphic mapping. With regard to potential theory, he will study properties of the complex Monge-Ampere operator and its relationship to the stability of the Dirichlet problem and to the pluri-complex Green function. With regard to dynamical systems, he will study the behavior of invertible polynomial mappings of complex Euclidean space, especially the equilibrium measure of the analog of the Julia set. And with regard to holomorphic mappings, he will try to classify the smoothly bounded domains that have noncompact automorphism groups.

首席研究员将继续研究涉及与势论、动力系统和全纯映射相关的多个复杂变量的函数的问题。 在势论方面，他将研究复数Monge-Ampere算子的性质及其与狄利克雷问题稳定性和复数格林函数的关系。 在动力系统方面，他将研究复杂欧几里得空间的可逆多项式映射的行为，特别是朱莉娅集类比的平衡测度。 关于全纯映射，他将尝试对具有非紧自同构群的平滑有界域进行分类。