Mathematical Sciences: Polynomially Convex Hulls and their Applications

9412392 Slodkowski这个建议中的问题与多项式有关 凸壳及其应用提议者打算 追求他的长期兴趣多项式船体纤维超过 单位圆他将特别集中精力分析 非连通纤维多项式壳的结构 找到新的应用。他还计划学习 二维或多维Levi方程的弱解 它们在描述多项式壳和 n维子流形的全纯包络 复欧氏空间 数学分析的作用是提供定性的， 有关的定量和几何信息 方程的解当方程定义在 多复变域的近似 函数和解决方案是复杂的几何形状的 域这个项目研究了 复杂的几何形状和近似。特别是，该项目 将适用于极端值的位置， 复杂方程的解。 ***

9412392 Slodkowski The problems in this proposal are concerned with polynomial convex hulls and their applications. The proposer intends to pursue his long term interest in polynomial hulls fibered over the unit circle. he will concentrate especially on analyzing the structure of polynomial hulls with non-connected fibers and finding their new applications. He also plans to study weak solutions of Levi equations in two or more dimensions and their applications to description of polynomial hulls and envelopes of holomorphy of submanifolds of n-dimensional complex Euclidean space. The role of mathematical analysis is to provide qualitative, quantitative and geometric information concerning the solutions of equations. When the equations are defined over domains in several complex variables the approximation of functions and solutions is complicated by the geometry of the domain. This project studies this interplay between the complex geometry and approximation. In particular, the project will have application to the location of extreme values of solutions to complex equations. ***