Mathematical Sciences: Research in Several Complex Variables and Application

9622285 Lempert拟议的研究涉及多个复变量领域。研究人员希望研究当Cauchy-Riemann结构被扰动时，Cauchy-Riemann流形的可嵌入性如何表现。此外，研究者计划研究无限维复流形的各种性质：希尔伯特空间中的非齐次Cauchy-Riemann方程、Newlander-Nirenberg定理的推广和Oka原理是所追求的主题之一。基于复数的空间出现在许多自然环境中。例如，一般的多项式方程只有在(有限维)复数空间中才能求解。所提出的研究涉及抽象复空间和无限维复空间。

9622285 Lempert The proposed research lies in the area of several complex variables. The investigator wishes to study how the property of embeddability of Cauchy-Riemann manifolds behaves when the Cauchy-Riemann structure is perturbed. In addition, the investigator plans to study various properties of infinite dimensional complex manifolds: the inhomogeneous Cauchy-Riemann equations in Hilbert spaces, the extension of the Newlander-Nirenberg theorem and the Oka principle are among the topics pursued. Spaces based on complex numbers arise in many natural settings. For example, polynomial equations in general can not be solved unless one works in a (finite dimensional) complex space. The proposed research deals with abstract complex spaces and infinite dimensional complex spaces.