Mathematical Sciences: Research in Circle Packings, Quasiconformal Geometry and Low Dimensional Geometric Topology

数学科学：圆堆积、拟共形几何和低维几何拓扑研究

• 批准号: 9006954
• 负责人: Zheng-Xu He
• 金额: $ 2.34万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9006954&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Circle; Packings

The principal investigator will study conformal moduli and the energy of incompressible flows, and the relationship between circle packings and the geometry of Riemann surfaces. The first project involves an investigation into how knot types of field lines restrict arbitrary decreases in the energy. The second project will be a continuation of earlier work on the convergence of derivatives for hexagonal packing schemes. The principal investigator will carry out two projects in the area of geometric complex analysis. The first involves a study of the behavior of fluid flow. In particular, he will analyze the manner in which a flow loses energy or slows down when flow lines are knotted. The second project involves the relationship between how a circle can be packed with smaller circles, and aspects of conformal complex analysis.

首席研究员将研究共形模量， 不可压缩流的能量，以及 圆填充和黎曼曲面几何。 第一 项目涉及到如何结类型的领域的调查 线限制能量的任意减小。 第二 该项目将是早期工作的延续， 六角填充方案的导数。 首席研究员将开展两个项目， 几何复分析领域。 第一个涉及到一个 研究流体流动行为的学科。 特别是，他将 分析流动损失能量或减速的方式 当流线打结时。 第二个项目涉及 一个圆如何被小的 圆和共形复分析的各个方面。