Quasiconformal Mappings, Doubling Measures and Subharmonic Functions

拟共形映射、倍增测度和次谐波函数

• 批准号: 9705227
• 负责人: Jang-Mei Wu
• 金额: $ 8.4万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2000-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9705227&HistoricalAwards=false
• 关键词: Quasiconformal; Mappings; Doubling; Measures; Subharmonic

Wu Abstract Professor Wu shall continue her study of removable sets and nonremovable sets for quasiconformal mappings. She intends to construct nonremovable sets which are simple in nature and can be described without using mappings. Such sets are known to exist in the plane, the problem here is for higher dimensional space. She also intends to study whether the lifting of sets from the plane into the space will destroy the nonremovability. Also Professor Wu shall continue her work on null sets of dyadic doubling measures: how easily a null set may be changed into a non-null set under the multiplication by a positive number. This problem has a close connection with a question of P. Erdos on universal sets. Furthermore, Professor Wu shall continue to investigate the growth of subharmonic functions in half space and its influence on the size of the asymptotic sets on the boundary. Professor Wu is working in the area of potential theory and geometric function theory. More specifically, she studies the growths of the solutions of certain differential equations, the geometry of the region where the equations are defined, and their relations. One of the equations under study is Laplace's equation, which has a very important place in the study of thermal conductivity, electrostatic potential and fluid dynamics. Moreover, this equation is the root of a whole family of differential equations, called elliptic equations. Elliptic equations are interesting to mathematicians due to their origins in physics.

吴 摘要 吴教授将继续她的研究活动集， 拟共形映射的不可去集。 她打算 构造本质上是简单的并且可以 不使用映射进行描述。 已知存在这样的集合 在平面上，这里的问题是高维空间。 她还打算研究是否解除集从 飞机进入太空会破坏不可移动性。 也 吴教授将继续她的工作，空集并矢 加倍措施：如何容易一个空集可以改变成一个 非空集下乘以一个正数。 这 这个问题与P.Erdos关于 万有集 此外，吴教授将继续 研究半空间中次调和函数的增长， 它对边界上渐近集的大小的影响。 吴教授从事势能理论研究， 几何函数论 更具体地说，她研究了 某些微分方程的解的增长， 定义方程的区域的几何形状及其 关系 研究中的一个方程是拉普拉斯方程 方程，这在研究中有一个非常重要的地位， 导热性、静电势和流体动力学。 此外，这个方程是一个完整的家庭的根， 微分方程，称为椭圆方程。 椭圆 方程对数学家来说很有趣，因为它们的起源 在物理学中。