Function Theory of Several Complex Variables

多复变量函数论

• 批准号: 2000050
• 负责人: Xiaojun Huang
• 金额: $ 21.2万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-06-01 至 2024-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2000050&HistoricalAwards=false
• 关键词: Function; Theory; Several; Complex; Variables

This project is about the understanding of complex-valued functions. Complex numbers and functions of complex variables have become, since the nineteenth century, indispensable tools in many areas of mathematics and its applications to other areas of science and engineering. The solutions of many problems in the applied sciences could ultimately depend on improvements in these complex analytic tools and in a deeper understanding of their basic properties. This project provides research training for graduate students, and the principal investigator will continue mentoring postdocs and organizing conferences on several complex variables and complex geometry, bringing together mathematicians to discuss their research and teaching.The principal investigator will work on several fundamental problems in complex analysis of several variables that are closely related to research in differential geometry, subelliptic analysis and classical dynamics. More specifically, he plans to continue his research on the equivalence problem and the rigidity problem in several complex variables, to carry further his work on the complex structure of the holomorphic hull of a real submanifold in a complex space, and to investigate various boundary CR invariants, including the famous Bloom conjecture in any dimension.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这个项目是关于对复值函数的理解。自世纪以来，复数和复变函数已经成为数学许多领域不可或缺的工具，并将其应用于其他科学和工程领域。应用科学中许多问题的解决最终可能取决于这些复杂分析工具的改进以及对其基本性质的更深入理解。该项目为研究生提供研究培训，首席研究员将继续指导博士后并组织关于多复变和复几何的会议，将数学家聚集在一起讨论他们的研究和教学。首席研究员将致力于与微分几何研究密切相关的多复变分析中的几个基本问题，亚椭圆分析和经典动力学。更具体地说，他计划继续他的研究等价问题和刚性问题在几个复变量，进一步进行他的工作的复杂结构的全纯船体的一个真实的子流形在一个复杂的空间，并调查各种边界CR不变量，包括著名的布卢姆猜想在任何维度。这个奖项反映了NSF的法定使命，并已被认为值得支持，使用基金会的知识价值和更广泛的影响审查标准进行评估。

项目成果

Complex geodesics and complex Monge–Ampère equations with boundary singularity

具有边界奇点的复杂测地线和复杂蒙日安培方程

• DOI: 10.1007/s00208-020-02111-4
• 发表时间: 2022
• 期刊: Mathematische Annalen
• 影响因子: 1.4
• 作者: Huang, Xiaojun;Wang, Xieping
• 通讯作者: Wang, Xieping

Regular multi-types and the Bloom conjecture

正则多型和布卢姆猜想

• DOI: 10.1016/j.matpur.2020.05.007
• 发表时间: 2021
• 期刊: Journal de Mathématiques Pures et Appliquées
• 作者: Huang, Xiaojun;Yin, Wanke
• 通讯作者: Yin, Wanke

Boundary characterization of holomorphic isometric embeddings between indefinite hyperbolic spaces

不定双曲空间之间全纯等距嵌入的边界表征

• DOI: 10.1016/j.aim.2020.107388
• 发表时间: 2020-11
• 期刊: Advances in Mathematics
• 影响因子: 1.7
• 作者: Xiaojun Huang;Jin Lu;Xiaomin Tang;Ming Xiao
• 通讯作者: Ming Xiao

Revisiting a Non-Degeneracy Property for Extremal Mappings

重新审视极值映射的非简并性质

• DOI: 10.1007/s10473-021-0602-6
• 发表时间: 2021
• 期刊: Acta Mathematica Scientia
• 影响因子: 1
• 作者: Huang, Xiaojun

Bergman–Einstein metrics, a generalization of Kerner’s theorem and Stein spaces with spherical boundaries

• DOI: 10.1515/crelle-2020-0012
• 发表时间: 2020-05
• 期刊: Journal für die reine und angewandte Mathematik (Crelles Journal)
• 作者: Xiaojun Huang;Ming Xiao