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A new development of complex analytic geometry by using Lie theory

Research Project

Project/Area Number 15K04913
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionTohoku University

Principal Investigator

Shimizu Satoru  東北大学, 理学研究科, 准教授 (90178971)

Project Period (FY) 2015-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywordsリー理論 / 複素解析幾何 / CR幾何 / 無限小CR自己同型 / チューブ領域 / ラインハルト領域 / 正則自己同型 / 正則同値問題
Outline of Final Research Achievements

In the present research, through the study of complex domains by using Lie theory, we obtained an interesting result on complex bounded domains called tube domains. To be concrete, under some general setting, when the holomorphic automorphism group of a tube domain is solvable, we clarified the structure of the group. Also, concrete examples of tube domains that have solvable holomorphic automorphism groups were not known well, but we could find an elementary example which can be understood even by high school student knowledge and has much importance.

Academic Significance and Societal Importance of the Research Achievements

数学においては、応用例のない定理や一般論はつまらない、と言われることがある。また数学は高度に抽象的な学問であることから、意義ある具体例というものは重要な意味をもつ。そのようなことから、本研究およびそれに連なる研究において、一般的な理論を構築するのみならず、その応用として意義ある具体例を与えることが出来たことは、学術的意義のあることと考えられる。またその具体例は一般的理論の構築なしでは得ることは出来なかったであろうことにも注意したい。

Report

(5 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (15 results)

All 2019 2018 2017 2016 2015

All Journal Article (7 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 7 results,  Acknowledgement Compliant: 1 results,  Open Access: 1 results) Presentation (8 results) (of which Int'l Joint Research: 1 results,  Invited: 1 results)

  • [Journal Article] Two theorems on the Fock-Bargmann-Hartogs domains2019

    • Author(s)
      Akio Kodama and Satoru Shimizu
    • Journal Title

      Osaka Journal of Mathematics

      Volume: 56

    • NAID

      120006768700

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cohomological Laplace transform on non-convex cones and Hardy spaces of d-bar cohomology on non-convex tube domains2018

    • Author(s)
      Simon Gindikin and Hideyuki Ishi
    • Journal Title

      Journal of Lie Theory

      Volume: 28 Pages: 245-263

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Structure and equivalence of a class of tube domains with solvable groups of automorphisms2017

    • Author(s)
      Satoru Shimizu
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 69 Issue: 3 Pages: 1157-1177

    • DOI

      10.2969/jmsj/06931157

    • NAID

      130005906740

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Bergman kernel function for Hartogs domains over bounded homogeneous domains2017

    • Author(s)
      Hideyuki Ishi, Jong-Do Park, Atsushi Yamamori
    • Journal Title

      The Journal of Geometric Analysis

      Volume: 27 Issue: 2 Pages: 1703-1736

    • DOI

      10.1007/s12220-016-9737-4

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Holomorphic equivalence problem for Reinhardt domains and the conjugacy of torus actions2016

    • Author(s)
      Satoru Shimizu
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 68 Pages: 273-291

    • NAID

      130008106145

    • Related Report
      2016 Research-status Report 2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A rigidity theorem for proper holomorphic mappings between generalized pseudoellipsoids2016

    • Author(s)
      Atsushi Hayashimoto
    • Journal Title

      Tokyo Journal of Mathematics

      Volume: 39 Pages: 389-421

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Classification of proper holomorphic mappings between generalized pseudoellipsoids of different dimensions2015

    • Author(s)
      Atsushi Hayashimoto
    • Journal Title

      Complex Analysis and Geometry, Springer Proceedings in Mathematics and Statics

      Volume: 144 Pages: 149-159

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Presentation] 等質有界領域の準局所的特徴付け2018

    • Author(s)
      清水 悟
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 可解な自己同型群をもつチューブ領域2017

    • Author(s)
      清水 悟
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2017 Research-status Report
  • [Presentation] 可解な自己同型群をもつチューブ領域2017

    • Author(s)
      清水 悟
    • Organizer
      多変数関数論冬セミナー
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] ヘッセ領域上の群不変ポテンシャル2017

    • Author(s)
      伊師英之, 小原敦美
    • Organizer
      日本数学会年会
    • Place of Presentation
      首都大学東京(東京都)
    • Related Report
      2016 Research-status Report
  • [Presentation] Bergman-Hartogs 領域上の調和解析2016

    • Author(s)
      伊師 英之
    • Organizer
      日本数学会年会
    • Place of Presentation
      筑波大学
    • Year and Date
      2016-03-17
    • Related Report
      2015 Research-status Report
  • [Presentation] 可解な自己同型群をもつある種のチューブ領域の構造と同値性2015

    • Author(s)
      清水 悟
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-15
    • Related Report
      2015 Research-status Report
  • [Presentation] 凸錐上の函数のラプラス変換とルジャンドル変換2015

    • Author(s)
      伊師 英之
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-14
    • Related Report
      2015 Research-status Report
  • [Presentation] Stability groups and decomposition of infinitesimal CR automorphisms of infinite type model in $C^2$2015

    • Author(s)
      林本 厚志
    • Organizer
      The 23rd International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
    • Place of Presentation
      九州産業大学
    • Year and Date
      2015-08-26
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research

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Published: 2015-04-16   Modified: 2020-03-30  

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