摘要
In the field of several complex variables, the Greene-Krantz Conjecture, whose consequences would be far reaching, has yet to be proven. The conjecture is as follows： Let D be a smoothly bounded domain in Cn. Suppose there exists {gj} C Aut（D） such that {gj（z）} accumulates at a boundary point p ∈δD for some z C D. Then DD is of finite type at p. In this paper, we prove the following result, yielding further evidence to the probable veracity of this important conjecture： Let D be a bounded convex domain in C2 with C2 boundary. Suppose that there is a sequence {gj} Aut（D） such that {gj（z）} accumulates at a boundary point for some point z ∈ D. Then if p E OD is such an orbit accumulation point, OD contains no non-trivial analytic variety passing through p.
In the field of several complex variables, the Greene-Krantz Conjecture, whose consequences would be far reaching, has yet to be proven. The conjecture is as follows: Let D be a smoothly bounded domain in Cn. Suppose there exists {gj} ? Aut(D) such that {gj(z)} accumulates at a boundary point p ∈ ?D for some z ∈ D. Then ?D is of finite type at p. In this paper, we prove the following result, yielding further evidence to the probable veracity of this important conjecture: Let D be a bounded convex domain in C^2 with C^2 boundary.Suppose that there is a sequence {gj} ? Aut(D) such that {gj(z)} accumulates at a boundary point for some point z ∈ D. Then if p ∈ ?D is such an orbit accumulation point, ?D contains no non-trivial analytic variety passing through p.
