UC Riverside

The problem of characterizing bounded domains in Cn is can be related to the automorphism group and the geometry of the boundary. It is a conjecture of Greene and Krantz that if a smoothly bounded domain has a noncompact automorphism group, then the boundary is of finite type at any automorphism accumulation point. While there have been numerous supporting results, the conjecture is as yet unsolved. The purpose of this dissertation is to provide another result in support of the Greene-Krantz conjecture. Specifically, if the boundary of a smoothly bounded convex domain admits an iterated automorphism orbit nontangentially, then it is of finite type.