Mathematical Sciences: Geometric and Analytic Problems in Several Complex Variables and Partial Equations

数学科学：多个复变量和偏方程的几何和解析问题

• 批准号: 9501516
• 负责人: Linda Rothschild
• 金额: $ 21万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501516&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Analytic; Problems

DMS-9501516 Rothschild/Baouendi The investigators will study the geometry of real submanifolds in complex space. In particular, they will focus on geometric and analytic invariants of these manifolds under holomorphic changes of coordinates. Special consideration will be given to those manifolds globally defined by real polynomial equations. For many manifolds defined by the vanishing of real polynomials, any component of a holomorphic transformation from one such manifold to another must also be a root of a complex polynomial. 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.

研究人员将研究复空间中实子流形的几何。特别地，他们将关注这些流形在全纯坐标变化下的几何不变量和解析不变量。将特别考虑由实多项式方程全局定义的流形。对于由实多项式的消失所定义的许多流形，从一个这样的流形到另一个这样的流形的全纯变换的任何分量也必须是复多项式的根。本世纪初出现了几个复变量，作为一个复变量函数研究的自然产物。很明显，这个理论与它的前身有很大的不同。底层的几何结构更难掌握，而函数理论与一阶偏微分算子的关系要密切得多。因此，它成长为一门混合学科，结合了微分几何和微分方程的深层特征。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。