Mathematical Sciences: Complex Manifolds and Meromorphic Mappings

数学科学：复流形和亚纯映射

• 批准号: 9500491
• 负责人: Bernard Shiffman
• 金额: $ 12.6万
• 依托单位: Johns Hopkins University
• 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: 1995-07-01 至 1998-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500491&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Complex; Manifolds; Meromorphic

DMS-9500491 Shiffman Shiffman will continue his research on complex varieties and meromorphic mappings. He will investigate the Kabayashi-Royden infinitesimal pseudometric and Kobayashi pseudodistane with a goal towards obtaining a better understanding of the concept of hyperbolicity for projective manifolds. He will also return to the topic of value distribution theory and will seek new defect relations for meromorphic maps and for sections of vector bundles. Several complex variables arose at the beginning of the century as a natural outgrowth of studies of functions of one complex variable. It became clear early on that the theory differed widely from it predecessor. The underlying geometry was far more difficult to grasp and the function theory had far more affinity with partial differential operators of first order. It thus grew as a hybrid subject combining deep characteristics of differential geometry and differential equations. Many of the fundamental structures were defined in the last three decades. Current studies still concentrate on understanding these basic mathematical forms.

DMS-9500491 Shiffman Shiffman 将继续他对复杂品种和亚态映射的研究。 他将研究 Kabayashi-Royden 无穷小伪度量和 Kobayashi 伪距离，目的是更好地理解射影流形的双曲性概念。 他还将回到值分布理论的主题，并为亚纯映射和向量丛的部分寻找新的缺陷关系。 本世纪初，作为一个复变量函数研究的自然产物，出现了几个复变量。 人们很早就发现该理论与其前身有很大不同。 底层的几何学更加难以掌握，而函数论与一阶偏微分算子的亲和力要强得多。 因此，它发展成为一门结合了微分几何和微分方程深层特征的混合学科。 许多基本结构是在过去三十年中定义的。 目前的研究仍然集中于理解这些基本的数学形式。