Mathematical Sciences: Problems Relating to the Circle Packing Theorem

数学科学：与圆堆积定理相关的问题

• 批准号: 9112150
• 负责人: Burton Rodin
• 金额: $ 3.52万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1993-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9112150&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Relating; Circle

The research supported by this award will investigate an approach to a conformal mapping theorem for non-Riemannian metrics. The principal investigator will try to extend the method of circle packing which was used to give a proof of the standard Riemann mapping theorem. He will also undertake a study of infinite circle packings and try to describe the relationship between the shape of an infinite circle packing with prescribed combinatorics and the rigidity of such a structure. This research is an extension of the classical theorem which says that a simply connected two dimensional domain, one without holes, is equivalent in a very precise way to a disk, a plane or a sphere. A method of proving this theorem involving a packing of the domain by circles was discovered several years ago. This research involves questions raised by this new proof. The theorem itself is used in a very crucial way in computing flow over airfoils and the recently discovered proof opens up new possibilities for more efficient computations of flows.

该奖项支持的研究将调查 非黎曼度量的共形映射定理的一种方法。 首席研究员将尝试扩展圆的方法 一种用于证明标准黎曼定理的包装 映射定理他还将研究无限循环 包装并尝试描述形状之间的关系 一个无限圆包装与规定的组合和 这种结构的刚性。 该研究是经典定理的推广， 说一个单连通的二维域，一个没有 孔，在一个非常精确的方式相当于一个磁盘，一个平面或 球体。证明这一定理的一种方法涉及到一个包装的 几年前就发现了圆域。本研究 这一新证据所引发的问题定理本身是 在计算翼型绕流时， 最近发现的证据为更多的人提供了新的可能性 流的高效计算。