Mathematical Sciences: The Pluri-Potential Theory and Its Application

在这个项目中，首席研究员将研究 多势理论中的各种问题， 复杂的分析。 这项工作的最终目标是 构造多重次调和不变边界理论 函数和全纯函数 特别是 首席研究员将研究多个边界属性， 关于Green-Martin拓扑的次调和函数， 多重次调和函数的位势分解 和极大函数，多项式壳的解析结构 和Wermer Alfreta。 次调和函数理论占有特殊的地位 在复变函数理论中，由于其内在的美， 因为它对其他领域也很重要 偏微分方程 在这个项目中，校长 研究人员将继续研究类似的理论， 所谓的“多重次谐波”函数。 复次谐波 函数出现在许多不同的环境中， 它们的性质将帮助我们理解一些问题， 微分几何和复变函数理论。

In this project the principal investigator will study various problems in pluri-potential theory that have applications to complex analysis. The ultimate goal of this work is to construct an invariant boundary theory for plurisubharmonic functions and holomorphic functions. In particular, the principal investigator will study boundary properties of pluri- subharmonic functions with respect to the Green-Martin topology, the decomposition of plurisubharmonic functions into potentials and maximal functions, the analytic structure of polynomial hulls and Wermer compacta. The theory of subharmonic functions occupies a special place in complex function theory because of its inherent beauty and because it is important to various other areas such as the theory of partial differential equations. In this project the principal investigator will continue working on an analogous theory for what are called "plurisubharmonic" functions. Plurisubharmonic functions arise in many different contexts, and a knowledge of their properties will help us understand a number of problems in differential geometry and complex function theory.