Loewner theory and holomorphic mappings in several variables

Loewner 理论和多变量的全纯映射

• 批准号: RGPIN-2015-04290
• 负责人: Graham, Ian
• 金额: $ 1.02万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=589709
• 关键词: Loewner; theory; holomorphic; mappings; several

The theory of univalent functions (i.e. one-to-one complex-analytic functions on the unit disc in the complex plane) is one of the most beautiful topics in one complex variable. There are many remarkable theorems dealing with extremal problems for this class of functions. Perhaps the most famous is the Bieberbach Conjecture for the Taylor series coefficients of univalent functions, solved in 1985 by Louis de Branges, but still sometimes known as the Bieberbach Conjecture. One of the most important techniques used to solve the Bieberbach Conjecture is a variational technique known as the Loewner method, in which a univalent function is embedded in an expanding flow of such functions governed by a differential equation.

单叶函数（即复平面上单位圆上的一对一复解析函数）理论是单复变函数中最美丽的课题之一。有许多显着的定理处理极值问题的这类功能。也许最著名的是比伯巴赫猜想的泰勒级数系数的单叶函数，解决了在1985年由路易斯德布兰日，但有时仍然被称为比伯巴赫猜想。用于解决比伯巴赫猜想的最重要的技术之一是被称为Loewner方法的变分技术，其中一个单叶函数嵌入在由微分方程控制的此类函数的扩展流中。