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.

该项目继续以几个复杂变量理论为中心的数学研究。 这项工作涉及对复杂流形的研究，代表几何观点，以及对复杂函数的价值分布和连续性特性的分析研究。 一个主要的重点是涉及所谓的Hartogs现象，从而在围绕域周围区域（例如在复杂的环中）定义的几个变量的全态函数继续作为内部区域的全体形态函数。 将在将这个想法扩展到两个方向时完成。 第一个是确定单独的分析性暗示关节的程度，而第二个分析性与Hartogs现象有关，因为它与映射到复杂的歧管有关。 尽管许多歧管反映了此属性，但有些不反映。 出色的问题仍然是目标歧管上的条件之一，以便将所有映射的扩展属性都纳入歧管。 价值分布理论与几个复杂变量的空间中定义的全体形态函数在多大程度上有关忽略或假设给定值的程度。 这种亲和力的测量涉及对本世纪最初几十年来为单个变量的函数开发的经典内凡林纳理论的概括。 对于非结构函数，它们对任何值的亲和力几乎总是与其他任何值相同。 例外代表功能的缺陷 - 在本研究期间，缺陷集的度量将是主要问题。