Study of holomorphic automorphism groups and its application to complex analysis

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540167
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tohoku University
• Principal Investigator: SHIMIZU Satoru 東北大学, 理学(系)研究科(研究院), 准教授 (90178971)
• Co-Investigator(Kenkyū-buntansha): KODAMA Akio 金沢大学, 理工研究域数物科学系, 教授 (20111320)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 関数論 / 正則自己同型群 / ラインハルト領域 / チューブ領域 / 複素幾何学 / 正則同値問題 / リー群 / 正則ベクトル場

Outline of Final Research Achievements

In the present research, through the study of the problem of characterizing complex manifolds by their holomorphic automorphism groups, we obtained an interesting result on Siegel domains of the first kind. To be concrete, we determined the form of diffeomorphisms between Siegel domains of the first kind preserving the holomorphic automorphism groups, and gave its applications. Also, the study of unbounded Reinhardt domains has made much progress. In particular, we could give an affirmative answer to the holomorphic equivalence problem for a certain fundamental class of unbounded Reinhardt domains, which is a long-pending problem.

Free Research Field

多変数複素解析学