Function Theory in Several Complex Variables

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

Research will be conducted on a number of problems in Several Complex Variables and Cauchy-Riemann Geometry. 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 surfaces in the complex space of dimension two, and the investigation of its intrinsic connections with many well-known problems in classical mechanics will be pursued. Complex numbers and functions of complex variables have become, since the 19th century, indispensable tools in many areas of mathematics and in its application to other areas of science and engineering. Indeed, the solutions of many problems in the applied sciences could ultimately depend on improvements in these complex analytic tools and a better understanding of their basic properties. For instance, in material science the standard method for treating multidirectional stresses in a uniform way is to represent them as complex numbers or, in more complicated 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 associated with these complex numbers or functions. Results of the research to be carried out in this project could lead to the discovery of new properties of solutions of these equations.