Quasiconformal Mappings, Doubling Measures and Subharmonic Functions

吴教授将继续研究拟共形映射的可移动集和不可移动集。她打算构造不可移动的集合，这些集合本质上是简单的，可以不使用映射来描述。已知这样的集合存在于平面中，这里的问题是对于高维空间。她还打算研究是否从飞机上抬起布景进入空间会破坏不可移动性。吴教授还将继续她关于并矢加倍测度的零集的研究：在正数的乘法作用下，零集如何容易地变成非零集。这个问题与泛集上的P. Erdos问题有密切的联系。此外，吴教授将继续研究半空间中次调和函数的增长及其对边界上渐近集大小的影响。吴教授主要从事势理论和几何函数理论的研究。更具体地说，她研究某些微分方程的解的增长，方程被定义的区域的几何，以及它们之间的关系。所研究的方程之一是拉普拉斯方程，它在热导率、静电势和流体动力学的研究中占有非常重要的地位。此外，这个方程是一组微分方程的根，称为椭圆方程。由于椭圆方程起源于物理学，数学家对它很感兴趣。

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.