Mathematical Sciences: Geometric Methods in the Theory of Functions

数学科学：函数论中的几何方法

• 批准号: 8701594
• 负责人: James Jenkins
• 金额: $ 6.33万
• 依托单位: Washington University
• 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: 1987-06-01 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701594&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Methods; Theory

In this project work will be done on self-conformal mappings of Riemann surfaces. In recent work the principal investigator has given a representation for arbitrary Riemann surfaces which provided simple proofs of old results together with new applications to self-conformal maps of surfaces which have a fixed point. In cases where the group of maps have several base points good progress has been made in describing the groups in terms of congruent polygons. Related to this work is on-going research measuring the number of regular mappings between a fixed (closed) Riemann surface to surfaces of lower genus. This finite bound depends only on the genus of the original surface. Similar questions regarding maps between multiply connected plane domains will be treated. The extremal metric method and Loewner's variational method of studying univalent functions have never been studied for connections. A careful analysis of this question will be undertaken. Aside from general interest, the outcome of this effort should provide a characterization of Loewner chains associated with quadratic differentials.

在此项目中，将对Riemann表面的自符号映射进行。 在最近的工作中，首席研究者为任意的Riemann表面提供了代表，该表面提供了旧结果的简单证明以及具有固定点的表面的自符号图。 如果图组具有多个基点的情况，则在描述一致多边形方面已经取得了良好的进步。 与这项工作相关的是正在进行的研究，测量了固定（封闭）riemann表面与较低属的表面之间的常规映射数量。 该有限结合仅取决于原始表面的属。 有关乘积连接的平面域之间地图的类似问题。 从未研究过与Loewner研究单价函数的各种方法的变异方法。 将对这个问题进行仔细的分析。 除了普遍的兴趣之外，这项工作的结果应提供与二次差异相关的洛夫纳链的特征。