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Function theory on q-pseudoconvex domains

Research Project

Project/Area Number 13640184
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionOsaka Women's University

Principal Investigator

MATSUMOTO Kazuko  Osaka Women's University, Science, Assistant Professor, 理学部, 助教授 (60239093)

Co-Investigator(Kenkyū-buntansha) O'UCHI Moto  Osaka Women's University, Science, Professor, 理学部, 教授 (70127885)
WATANABE Tokashi  Osaka Women's University, Science, Professor, 理学部, 教授 (20089957)
ISHIHARA Kazuo  Osaka Women's University, Science, Professor, 理学部, 教授 (90090563)
YOSHITOMI Kentaro  Osaka Women's University, Science, Lecturer, 理学部, 講師 (10305609)
IRIYE Kouyemon  Osaka Women's University, Science, Professor, 理学部, 教授 (40151691)
Project Period (FY) 2001 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2003: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2001: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywordsq-convex / levi form / plurisubharmonic / metric / several complex variables / 擬凸領域 / Levi形式 / 多変数関数論 / 複素解析学 / 多変数複素解析 / q-convex / Levi平坦曲面
Research Abstract

The results are the following:
(1)The intersection of finite number of q-complete domains is cohomologically (q^^〜1)-complete if q does not devide n. This is best and shaper than that obtained by the approximation theorem of Diederich-Fornaess and the vanishing theorem of Andreotti-Grauert.
(2)The complements of Levi flat real hypersurfaces in the complex tori of dimension 2 are Stein if they contain a local complex hypersurface which is not linear. This is the essential step to approach to the conjecture that there exists no Levi flat real hypersurfaces in complex tori except restricted types.
(3)For a given complex submanifold M in C^n, we expressed the Hermitian matrix determined by the Levi form of the function -log d by using the defing function of M, where d denotes the distance to M. As its application, the degeneracy condition of the Levi form is equivalent to that of Gauss map.
(4)For a given real submanifold M in C^2,we find a necessary and sufficient condition that the Levi form of distance to M degenerates. By applying this result, the Levi problem for complex tori can affimatively solved except the examples pointed out by Grauert.

Report

(4 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (37 results)

All Other

All Publications (37 results)

  • [Publications] Kazuko Matsumoto, Takeo Ohsawa: "On the real analytic Levi flat hypersurfaces in complex tori of dimension two,"Annales de l'Institute Fourier, Universite Grenoble I. 52. 1525-1532 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kazuko Matsumoto: "On the cohomological completeness of q-complete domains with corners"Nagoya Mathematical Journal. 168. 105-112 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kazuko Matsumoto: "Some geometric properties of Levi form of distance to real hypersurfaces in C^2"Japanese Journal of Mathematics. 30. (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kazuko Matsumoto: "Levi form of logarithmic distance to complex submanifolds and its application to developability"Advanced Studies in Pure Mathematics.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kazuo Ishihara: "Iterative methods for eigenvalue probeems with nondefferentisble normalization condition of a general complex matrix"Computing Supplementum. 15. 105-118 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kazuo Ishihara: "Descent iterations for improving approximate eigenpairs of polynomial eigenvalue problems with general complex matrices"Computing. 68. 239-254 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takashi Watanebe: "On the Bott suspension map for non-compact Lie groups"Journal of Mathematics of Kyoto University. 43. (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Moto O'uchi: "Pseudo-multiplicative unitaries on Hilbert C^*-modules"Far East Journal of Mathematical Sciences. Specil Vo.. 229-249 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Moto O'uchi: "Pseudo-multiplicative unitaries associated with inclusions of finite-dimensional C^*-algebras"Linear Algebra and its Applications. 341. 201-218 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Moto O'uchi: "Pentagonal equations for operators associated with inclusions of C^*-algebras"Scientiae Mathematicae Japonicae. 56. 71-94 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Moto O'uchi: "Coring structures associated with multiplicative unitary operators on Hilbert C ^*-modules"Far East Journal of Mathematical Sciences. 11. 121-136 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kouyemon Iriye: "The first derived functor of the inverse limit and localization"Journal of Pure and Applied Algebra. 173. 7-14 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kouyemon Iriye: "On phantom maps into suspension spaces"Journal of Mathematics of Kyoto University. 43. (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Matsumoto, T.Ohsawa: "On the real analytic Levi flat hypersurfaces in complex tori of dimension two"Annales de l'Institute Fourier, Universite Grenoble I. 52-5. 1525-1532 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Matsumoto: "On the cohomological completeness of q-complete domains with corners"Nagoya Mathematical Journal. 168. 105-112 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Matsumoto: "Some geometric properties of Levi form of distance to real hypersurfaces in C^2"Japanese Journal of Mathematics (New Series). 30-1(印刷中). (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Matsumoto: "Levi form of logarithmic distance to complex submanifolds and its application to developability"Complex Analysis in Several Variables, Advanced Studies in Pure Mathematics (eds. by K.Miyajima et al.) (Mathematical Society of Japan). (掲載決定).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Ishihara: "Iterative methods for eigenvalue problems with nondifferentiable normalized condition of a general complex matrix"Computing Supplementum. 15. 105-118 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Ishihara: "Descent iterations for improving approximative eigenpairs of polynomial eigenvalue problems with general complex matrices"Computing. 68. 239-254 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Watanabe: "On the Bott suspension map for non-compact Lie groups"Journal of Mathematics of Kyoto University. 43(印刷中). (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.O'uchi: "Pseudo-multiplicative unitaries on Hilbert C^*-modules"Far East Journal of Mathematical Sciences, Special Volume, Part 2 (Functional Analysis and its Applications). 229-249 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.O'uchi: "Pseudo-multiplicative unitaries associated with inclusions of finite-dimensional C^*-algebras"Linear Algebra and its Applications. 341. 201-218 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.O'uchi: "Pentagonal equations for operators associated with inclusions of C^*-algebras"Scientiae Mathematicae Japonicae. 56. 71-94 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.O'uchi: "Coring structures associated with multiplicative unitary operators on Hilbert C^*-modules"Far East Journal of Mathematical Sciences. 11. 121-136 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Iriye: "The first derived functor of the inverse limit and localization"Journal of Pure and Applied Algebra. 173. 7-14 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Iriye: "On phantom maps into suspension spaces"Journal of Mathematics of Kyoto University. 43(印刷中). (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kazuko Matsumoto: "Some geometric properties of Levi form of distance to real hypersurfaces in C^2"Japanese Journal of Mathematics. 30・1. (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Kazuko Matsumoto: "Levi form of logorithmic distance to complex submanufolds and its application to developability"Advanced Studies in Pure Mathematics. (近刊).

    • Related Report
      2003 Annual Research Report
  • [Publications] Moto O'uchi: "Coring structures associated with multiplicative unitary operators on Hilbert C^*-modules"For East Journal of Mathematical Sciences. 11・2. 121-136 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Takashi Watanabe: "On the Bott suspension map for non-compact Lie groups"Journal of Mathematics of Kyoto University. 43・4. (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Kouyemon Iriye: "On phantom maps into suspension spaces"Journal of Mathematics of Kyoto University. 43・4. (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Kazuko Matsumoto: "On the cohomological completeness of q-complete domains with corners"Nagoya Mathematical Journal. 168. 105-112 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Matsumoto, T.Ohsawa: "On the real analytic Levi flot hypersurfaces in complex tori of dimension two"Annales de l'Institut Fourier Univ. Grenoble I. 52・5. 1525-1532 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kazuko Matsumoto: "On the cohomological completeness of q-complete domains with corners"Nagoya Mathematical Journal. (掲載予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] Moto O'uchi: "Pseudo-multiplicative unitories associated with inclusions of finite-dimensional C^*-algebras"Linear Algebra and its Applications. 341. 201-218 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kazuo Ishihara: "Iterative methods for eigenvalue problemo with nondifferentiable normalized condition of a general complex"Computing Supplementum. 15. 105-118 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kazuo Ishihara: "Descent iterations for improving approximate eignpairs of polynomial eigenevalue problems with general comple N matrices"Computing. (掲載予定). (2002)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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