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Global complex analysis - around L^2 holomorphic functions

Research Project

Project/Area Number 14340041
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionNagoya University

Principal Investigator

OHSAWA Takeo  Nagoya University, Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (30115802)

Co-Investigator(Kenkyū-buntansha) MIYAKE Masatake  Nagoya University, Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (70019496)
SUZUKI Nariaki  Nagoya University, Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (50154563)
吉川 謙一  東京大学, 大学院・数理科学研究科, 助教授 (20242810)
平地 健吾  東京大学, 大学院・数理科学研究科, 助教授 (60218790)
中西 敏浩  名古屋大学, 大学院・多元数理科学研究科, 助教授 (00172354)
神本 丈  九州大学, 大学院・数理学研究科, 助教授 (90301374)
高山 茂晴  九州大学, 大学院・数理学研究科, 助教授 (20284333)
Project Period (FY) 2002 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥13,600,000 (Direct Cost: ¥13,600,000)
Fiscal Year 2005: ¥4,900,000 (Direct Cost: ¥4,900,000)
Fiscal Year 2004: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2003: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2002: ¥3,100,000 (Direct Cost: ¥3,100,000)
Keywordscomplex manifolds / holomorphic vector bundle / extension theorem / Levi flat / Kahler manifolds / Stein manifolds / コモホロジー入射性定理 / ∞でのベルグマン核の挙動 / レヴィ平坦超曲面 / 2次元複素トーラス / L^2正則関数 / Bergman計量 / 変形剛性 / Bergman空間 / 強擬凸領域 / Hardy空間 / コホモロジー入射性定理 / モデル領域 / 漸近解析 / Bergman核 / 擬凸領域
Research Abstract

Let M be a complex manifold, let S be a complex analytic subset of M and let E →M be a holomorphic vector bundle. Concerning the extension problem for holomorphic sections of E from S to M, we obtained the following.
Theorem, Let M be a weakly 1-complete Kahler manifold, let (E, h) be a Hermitian holomorphic vector bundle over M, and let (L, b) be a Hermitian holomorphic line bundle over M. For the curvature forms 【encircled H】_h and 【encircled H】_b of h and b, assume that 【encircled H】_h 【greater than or equal】 0 and 【encircled H】_h-εId_E【cross product】【encircled H】_b hold for some ε>0. Then, for any nonzero holomorphic section S of L, the homomorphism s : H^q(M, K_M【cross product】E) →H^q(M, K_M【cross product】E【cross product】L) has a kernel contained in the closure of zero.
We obtained also several results on Levi flat hypersurfaces.

Report

(5 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (13 results)

All 2006 2005 2004 Other

All Journal Article (6 results) Book (2 results) Publications (5 results)

  • [Journal Article] On a curvature condition that implies a cohomology injectivity theorem of Kollar-Skoda type2005

    • Author(s)
      Takeo Ohsawa
    • Journal Title

      Publ. Res. Inst. Math. Sci. 41

      Pages: 565-577

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On a curvature condition that implies a cohomology injectirity theorem of Kolla-Skoda type.2005

    • Author(s)
      Takeo Ohsawa
    • Journal Title

      Publ.RIMS 41

      Pages: 565-577

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On a curvature condition that implies a cohomology injectivity theorem of Kollar-Skoda type2005

    • Author(s)
      Takeo Ohsawa
    • Journal Title

      Publ.Res.Inst.Math.Sci. 41

      Pages: 565-577

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Behavior of the Bergman kernel at infinity2004

    • Author(s)
      B.Y.Chen, J.Kamimoto, T.Ohsawa
    • Journal Title

      Mathematische Zeitschrift 248

      Pages: 695-708

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On a curvature condition that implies a cohomology injectivity theorems of Kollar-Skoda type

    • Author(s)
      Takeo Ohsawa
    • Journal Title

      Publ.RIMS, Kyoto Univ. (発表予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On the Levi-flats in complex tori of dimension two

    • Author(s)
      Takeo Ohsawa
    • Journal Title

      Publ.RIMS, Kyoto Univ. (発表予定)

    • NAID

      110004626179

    • Related Report
      2004 Annual Research Report
  • [Book] 複素解析幾何と∂^^-方程式2006

    • Author(s)
      大沢健夫
    • Total Pages
      211
    • Publisher
      培風館
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Book] Complex analytic geometry and ∂^^- -equation (in Japanese)2005

    • Author(s)
      Takeo Ohsawa
    • Total Pages
      211
    • Publisher
      Baifukan
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Publications] Ohsawa, T.: "On the extension of L^2 holomorphic functions VI -a limiting case"Contemporary Math.. 332. 235-239 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Chen, B.-Y., Kamimoto, J., Ohsawa, T.: "Behavior of the Bergman Kernel at infinity"Math.Zeitschrift. (発表予定)(to appear).

    • Related Report
      2003 Annual Research Report
  • [Publications] Ohsawa, T.: "A precise L^2 division theorem"complex Geometry, collection of ps.d.t.H.Grauert. 185-191 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Diedrich, K., Ohsawa, T.: "On certain exsitence questions for pseudoconvex hypersurfaces"Math. Ann.. 323. 397-403 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Ohsawa, T.: "Analysis of Several Complex Variables"American Mathematical Society. 121 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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