Function Theory in Several Complex Variables

将对多个复变量和柯西-黎曼几何中的一些问题进行研究。更具体地说，将有助于更好地理解复分析和复几何中的各种刚性现象，研究真实曲面在二维复空间中的解析结构，并探索其与经典力学中许多著名问题的内在联系。自19世纪以来，复变量的复数和复变函数在许多数学领域以及在其他科学和工程领域的应用中已成为不可或缺的工具。实际上，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和对其基本性质的更好理解。例如，在材料科学中，统一处理多方向应力的标准方法是将它们表示为复数，或者在更复杂的情况下，表示为复杂函数。例如，材料中裂纹扩展的方向与某些方程的性质有关，这些方程与这些复数或函数有关。本项目的研究结果可能导致这些方程解的新性质的发现。

Research will be conducted on a number of problems in Several Complex Variables and Cauchy-RiemannGeometry. More specifically, the better understanding of various rigidity phenomena in complex analysis and complex geometry will be sought.The study the analytic structure of real surfacesin the complex space of dimension two, and the investigation of its intrinsic connections with many well-known problems in classical mechanicswill be pursued. Complex numbers and functions of complex variableshave become, since the 19th century, indispensabletools in many areas of mathematics and in itsapplication to other areas of science and engineering.Indeed, the solutions of many problems in the appliedsciences could ultimately depend on improvements in these complex analytic tools and a betterunderstanding of their basic properties. For instance,in material science the standard method for treatingmultidirectional stresses in a uniform way is to represent them as complex numbers or, in morecomplicated situations, as complex functions. It then turns out, for instance, that the direction of the propagation of cracks in materials is related to the properties of certain equations associatedwith these complex numbers or functions. Results of the research to be carried out in this project couldlead to the discovery of new propertiesof solutions of these equations.