Mathematical Sciences: Function Theory in Several Complex Variables

数学科学：多复变量函数论

• 批准号: 9500881
• 负责人: Xiaojun Huang
• 金额: $ 3.75万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500881&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Function; Theory; Several

DMS-9500881 Huang Huang will study the mapping problems for real hypersurfaces in complex spaces and try to prove various regularity results for Cauchy-Riemann mappings. He will investigate the smooth and analytic structure of a real submanifold in the complex space and the structure of its local hull of holomorphy. Also he will explore the Kobayashi extremal mappings of bounded domains in complex n-space and their applications to the study of holomorphic self-mappings. 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-9500881 Huang 黄将研究复空间中真实的超曲面的映射问题，并试图证明柯西-黎曼映射的各种正则性结果。 他将研究光滑和解析结构的真实的子流形在复杂的空间和结构的局部船体的全纯性。 此外，他将探讨小林极值映射的有界域在复杂的n-空间和他们的应用研究的全纯自映射。 多复变出现在世纪初作为一个自然的产物研究的职能，一个复杂的变量。 很明显，这个理论与它的前身有很大的不同。 基本的几何是更难以把握和函数理论有更多的亲和力与偏微分算子的一阶。 因此，它成长为一个混合学科结合了微分几何和微分方程的深刻特点。 许多基本结构是在过去三十年中确定的。 目前的研究仍然集中在理解这些基本的数学形式。