Uniformly Starlike Mappings And Uniformly Convex Mappings On The Four Kinds Of Classical Domains

The starlike mappings and the convex mappings are the main research objects in thegeometric function theory of several complex variables. The uniformly starlike mappingsand uniformly convex mappings are the extension of starlike mappings and convex map-pings. This thesis mainly study the uniformly starlike mappings and uniformly convexmappings on the four kinds of classical domains. The whole thesis contains three chapters.In the first chapter, we introduce briefly the background of the development of the ge-ometric function theory in several complex variables, some notations, definitions, lemmas,and the main results of the thesis.In the second chapter,we extend the definition of uniformly starlike mappings in theunit ball Bnto which is a bounded domain containing the origin,and we give a dis-criminant condition.Then we use the result to calculate the uniformly starlike mappings’discriminant conditions on the four kinds of classical domains.In the second chapter,we extend the definition of uniformly convex mappings inthe unit ball Bnto which is a bounded domain containing the origin,and we give adiscriminant condition.Then we use the result to calculate the uniformly convex mappings’discriminant conditions on the four kinds of classical domains.