Mathematical Sciences: Geometric Properties of Domains, Extremal Quasiconformal Mappings and Integrability of Conformal Mappings

数学科学：域的几何性质、极值拟共形映射和共形映射的可积性

• 批准号: 9203407
• 负责人: John Garnett
• 金额: $ 1.8万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-15 至 1994-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203407&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Properties; Domains

This award provides support for postdoctoral research on problems arising in the general area of geometric function theory. The work focuses on the geometric properties of quasiextremal distance domains. These are domains characterized by the property that points and closed sets can be joined by curves within the domain whose lengths do not be arbitrarily long. They are singled out because they have the characteristics believed to be fundamental for the study of quasiconformal mappings. Work on this project will concentrate on showing how the modulus of quasiextremal distance domains carries over to the dilatation constant for quasiconformal mapping defined on them. A second line of research will consider the length of level sets of univalent mappings and the question of the largest power to which such a mapping's derivative has a finite integral. Complex function theory encompasses the study of differentiable functions of a complex variable and related classes of functions such as harmonic functions and quasiconformal mappings. The subject is highly geometric; many of the problems concern the properties of various sets under transform by functions from one of the above classes. Applications of the theory to potential theory and fluid dynamics is now standard in engineering circles

该奖项为博士后研究提供支持， 几何函数一般领域中出现的问题 理论 这项工作的重点是几何性质的 拟极值距离域 这些领域的特点是 点和闭集可以通过 长度不是任意的域内曲线 久了 他们被挑出来是因为他们有 被认为是研究拟共形问题的基础 映射。 这个项目的工作将集中在展示如何 拟极值距离域的模传递到 定义在其上的拟共形映射的伸缩常数。 第二条研究线将考虑水平集的长度 单叶映射的最大幂问题 这样的映射的导数有有限积分。 复变函数理论包括研究 复变量的可微函数及相关函数 函数类，如调和函数和 拟共形映射 这个问题是高度几何;许多 的问题有关的性质，各种集下 通过上述类之一的函数进行转换。 该理论在势理论和流体力学中的应用 现在是工程界的标准