Quasiconformal Mappings, Doubling Measures and Subharmonic Functions

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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.