Characterization of convex domains in C2 with non-compact automorphism group

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（6）
• 页码范围: 977-984
• 页数: 8页
• 语种: 英文
• DOI: 10.1007/s11425-016-9031-6

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 ∈ (б)D for some z ∈ D.Then (б)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 C2 with C2 boundary.Suppose that there is a sequence {gj} C Aut(D) such that {gj(z)} accumulates at a boundary point for some point z ∈ D.Then if p ∈ (б)D is such an orbit accumulation point,(б)D contains no non-trivial analytic variety passing through p.