Pluripotential Theory, Hulls and Foliations

多能理论、船体和叶状结构

• 批准号: 125787714
• 负责人: Professor Dr. Nikolay Shcherbina
• 金额: --
• 依托单位: Fakultät für Mathematik und Naturwissenschaften
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/125787714?language=en
• 关键词: Pluripotential; Theory; Hulls; Foliations

Classical potential theory was built in the first part of the last century and its development was motivated mainly (but not only) by interests of electro-physics. Pluripotential theory is much younger and its basic results were obtained in 70’s - 80’s in the fundamental works of Bedford, Taylor, Sadullaev and others. Interest to this area and its importance are determined both by the needs of complex analysis and by applications to other fields, e.g. to dynamical systems. While many fundamental results of this theory are already well understood, we will address some important open problems concerning the structure of pluripolar sets and properties of the pluricomplex Green function. A second part of the project is devoted to the study of polynomial and rational hulls which appear naturally in the classical problem of polynomial and rational approximation. Despite the importance of these notions, the structure of polynomial and rational hulls is far from being understood even in the case of compact sets in Cn and is basically not understood at all for unbounded sets. Financial support for this project is aimed at fostering international collaboration, exchange of ideas, and especially (and foremost) at promoting young mathematicians.

经典势能理论建立于上个世纪的上半叶，它的发展主要（但不仅仅）是由电物理学的兴趣推动的。多能理论较年轻，其基本结果是在70 - 80年代由贝德福德、泰勒、萨杜拉耶夫等人的基础工作中得到的。对这一领域的兴趣及其重要性取决于复分析的需要和在其他领域的应用，例如动力系统。虽然这个理论的许多基本结果已经很好地理解，我们将解决一些重要的开放问题的结构的pluripolar集和性质的pluicomplex绿色函数。该项目的第二部分是专门研究自然出现在多项式和有理逼近的经典问题的多项式和有理外壳。尽管这些概念很重要，但多项式和有理壳的结构甚至在Cn中的紧集的情况下也远未被理解，并且对于无界集基本上根本不被理解。对该项目的财政支持旨在促进国际合作，交流思想，特别是（最重要的）促进年轻数学家。