Mathematical Sciences: Research in Geometrical Analysis

哈维教授是从微分几何角度进行复变分析的顶尖研究人员之一。他和他的同事们开发了一个新的几何学分支--校准，它应用于凯利几何和旋量。他建议继续他在校准几何方面的工作，特别是关于最小化面积的子流形。波尔金教授是求解含有多个复变量的偏微分方程组的专家。他和Harvey一起构造了复杂Neumann问题的显式核是一项重要的工作。波尔金建议继续他的工作，用显式核来求解多个复变量的柯西-黎曼方程和相关方程。哈维教授是涉及复杂分析的微分几何领域的世界领先者，并与合作者一起开发了一个新的几何领域，称为校准几何。标定后的几何形状具有绝对面积最小化的性质。哈维教授建议继续他对这一令人兴奋的新主题的研究，这将导致重要的结果。波尔金教授是解决多个复变量的偏微分方程组的专家。他建议继续他在这一领域的研究，为鲜为人知的问题寻找方程的解。很好地理解这些问题将是非常有意义的。

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.