Boundary Characterization of a Smooth Domain with Non-Compact Automorphism Group
One of the most important problems in the field of several complex variables is the Greene-Krantz conjecture:
Conjecture Let D be a smoothly bounded domain in Cn with non-compact automorphism group. Then the boundary of D is of finite type at any boundary orbit accumulation point.
The purpose of this dissertation is to prove a result that supports the truthfulness of this conjecture:
Theorem Let D be a smoothly bounded convex domain in Cn. Suppose there exists a point p in D and a sequence of automorphisms of D, f j, such that f j(p) &rarr q in the boundary of D non-tangentially. Furthermore, suppose Condition LTW holds. Then, the boundary of D is variety-free at q.