Mathematical Sciences: Research in Geometrical Analysis

点击翻译按钮获取中文摘要

Professor F. R. Harvey is one of the top researchers in complex analysis from the viewpoint of differential geometry. With his coworkers he has developed a new branch of geometry-- calibrations, which has applications to Cayley geometry and spinors. He proposes to continue his work on calibrated geometry, particularly with regard to area minimizing submanifolds. Professor J. C. Polking is an expert regarding the solution of partial differential equations containing several complex variables. His construction with Harvey of an explicit kernel for the complex Neumann problem is an important piece of work. Polking proposes to continue his work on explicit kernels for solving the Cauchy-Riemann equations and related equations in several complex variables. Professor Harvey is a world-leader in the field of differential geometry involving complex analysis and has developed with collaborators a new field of geometry, known as calibrated geometry. Calibrated geometries possess the property of absolute area minimizing. Professor Harvey proposes to continue his research on this exciting new topic which should lead to important results. Professor Polking is an expert on solving partial differential equations in several complex variables. He proposes to continue his research in this area by looking for the solutions of equations for problems for which very little is known. A good understanding of these problems would be of great interest.