Mathematical Sciences: Geometric Analysis: Research and Conformal Mapping, Extremal Length, and Riemann Surfaces

数学科学：几何分析：研究和共形映射、极值长度和黎曼曲面

• 批准号: 8701196
• 负责人: Burton Rodin
• 金额: $ 8.51万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1991-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701196&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Analysis; Research

Burton Rodin will continue investigations into a newly developed computational approach to the Riemann mapping theorem. This follows from the discovery of connections between conformal mapping and circle packing. Such investigations should lead to new insights into both areas and to new techniques in numerical conformal mapping. In addition research will be carried out into other areas of geometric function theory. This research will involve investigations into the following areas: the relationship between the boundary behavior of the Riemann mapping function and the geometry of the region; the application of Brownian excursion laws in the study of conformal mapping; holomorphic and quasiconformal families of Riemann mapping functions; harmonic measure estimates; the conformal mapping of curvilinear polygons; extremal length and harmonic measure relationships.

伯顿·罗丹将继续研究一种新开发的黎曼映射定理的计算方法。这源于保角映射和圆填充之间的联系的发现。这样的研究应该会为这两个领域带来新的见解，并带来数值保角映射的新技术。此外，还将对几何函数理论的其他领域进行研究。这项研究将涉及以下方面的研究：黎曼映射函数的边界行为与区域几何之间的关系；布朗游程定律在保角映射研究中的应用；黎曼映射函数的全纯族和拟共形族；调和测度估计；曲线多边形的保形映射；极值长度和调和测度关系。