Mathematical Sciences: Complex Manifolds and Meromorphic Mappings

该项目继续围绕数学研究， 多复变量理论中的一些问题。 工作 涉及复杂流形的研究，代表几何 观点，以及对价值的分析研究 复变函数的分布和连续性。 一个主要的焦点是所谓的哈托格人 多变量全纯函数 定义在域周围的区域中（例如在复合物中 环）作为内部区域的全纯函数继续。 将在两个方向上扩展这个想法。 的 首先是确定一个单独的分析性 第二种是指联合，而第二种是指哈托格人。 现象，因为它涉及到映射到复杂的流形。 虽然许多流形反映了这一性质，但也有一些没有。 的 一个突出的问题仍然是， 目标流形，使延伸性质保持所有 映射到流形上。 价值分配理论关注的是 其中定义在多个空间中的全纯函数 复杂变量可以省略或假定给定值。 的 这种亲和性的测量涉及对 经典的Nevanlinna理论是为函数而发展的， 在这个世纪的头几十年里， 为 非常数函数，它们对任何值的亲和力几乎都是 总是和其他人一样。 例外情况代表 函数的缺陷-集合的测度 在此期间，缺陷将是主要关注的问题。 调查

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.