Studies on intermediate pseudoconvexity in complex spaces

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K05301
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Hiroshima University
• Principal Investigator: ABE Makoto 広島大学, 先進理工系科学研究科(理), 教授 (90159442)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: 中間的擬凸性 / 正規複素空間 / Ｋ正則包 / ｎルンゲ性 / 単葉型開リーマン面 / 正則近似

Outline of Final Research Achievements

Regarding pseudoconvexity and intermediate pseudoconvexity for complex manifolds or for complex spaces, there are still many problems that need to be solved. In this study, we obtained a characterization for unramified domains over the space of n-tuples of complex numbers using quadratic functions to satisfy the intermediate pseudoconvexity. In addition, we obtained some new results on the n-Rungeness for open sets in n-dimensional complex manifolds, on planar open Riemann surfaces, and on the K-envelopes of holomorphy of K-complete normal complex spaces.

Free Research Field

多変数関数論・複素解析幾何

Academic Significance and Societal Importance of the Research Achievements

この研究において得られたいくつかの成果，例えば，ｎ個の複素数の組全体のなす空間の上の不分岐領域が中間的擬凸性をみたすための新しい特徴付けについては，それがもっと一般的な状況における擬凸性・中間的擬凸性の考察のための応用の可能性をもつことなど，多変数関数論・複素解析幾何の今後の一定の発展のために寄与するためのいくつか緒であることが期待される．