Mathematical Sciences: Complex Manifolds and Meromorphic Mappings

数学科学：复流形和亚纯映射

• 批准号: 9001365
• 负责人: Bernard Shiffman
• 金额: $ 8.32万
• 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: 1990
• 资助国家: 美国
• 起止时间: 1990-04-01 至 1992-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001365&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Complex; Manifolds; Meromorphic

This project continues mathematical research centering on topics in the theory of several complex variables. The work involves studies of complex manifolds, representing the geometric point of view, together with analytic investigations into value distributions and continuity properties of complex functions. One primary focus concerns what is known as the Hartogs phenomenon whereby a holomorphic function of several variables defined in a region surrounding a domain (such as in a complex annulus) continues as a holomorphic function to the inner region. Work will be done in extending the idea in two directions. The first is to determine the extent to which a separate analyticity implies joint, while the second is concerned with the Hartogs phenomenon as it relates to mapping into complex manifolds. Although many manifolds reflect this property, some do not. The outstanding problem remains one of giving conditions on the target manifolds so that the extension property holds for all mappings into the manifold. Value distribution theory is concerned with the extent to which holomorphic functions defined in the space of several complex variables can omit or assume given values. The measurement of such affinities involves generalizations of the classical Nevanlinna theory which was developed for functions of a single variable during the first decades of this century. For nonconstant functions, their affinity for any value is almost always the same as for any other. The exceptions represent the deficiencies of the function - the measure of the set of deficiencies will be of primary concern during this investigation.

该项目继续以多个复变量理论主题为中心的数学研究。 这项工作涉及对代表几何观点的复流形的研究，以及对复函数的值分布和连续性特性的分析研究。 一个主要关注点涉及所谓的哈托格斯现象，即在域周围的区域（例如在复环中）中定义的多个变量的全纯函数继续作为内部区域的全纯函数。 将在两个方向上扩展这一想法。 第一个是确定单独的分析性意味着联合的程度，而第二个则涉及哈托格斯现象，因为它与映射到复杂流形有关。 尽管许多流形反映了此属性，但有些流形却没有。 突出的问题仍然是在目标流形上给出条件，以便扩展属性适用于到流形的所有映射。 值分布理论涉及在多个复变量空间中定义的全纯函数可以忽略或假定给定值的程度。 这种亲和力的测量涉及经典 Nevanlinna 理论的概括，该理论是在本世纪头几十年针对单个变量的函数而发展起来的。 对于非常量函数，它们对任何值的亲和力几乎总是与对任何其他值的亲和力相同。 异常代表了功能的缺陷 - 缺陷集的度量将是本次调查期间主要关注的问题。