• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

1988 Fiscal Year Final Research Report Summary

Analysis on Complex Manifold

Research Project

Project/Area Number 62302003
Research Category

Grant-in-Aid for Co-operative Research (A)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionTOKYO INSTITUT OF TECHNOLOGY

Principal Investigator

NOGUCHI Junjiro  Faculty of Science, Tokyo Institut of Technology, 理学部, 教授 (20033920)

Co-Investigator(Kenkyū-buntansha) KAZAMA Hideki  College of General Education, Kyushu University, 教養部, 助教授 (10037252)
TANIGUCHI Masahiko  Faculty of Science, Kyoto University, 理学部, 助教授 (50108974)
IMAYOSHI Yoichi  College of General Education, Osaka University, 教養部, 助教授 (30091656)
ITO Masayuki  College of General Education, Nagoya University, 教養部, 教授 (60022638)
SUITA Nobuyuki  Faculty of Science, Tokyo Institut of Technology, 理学部, 教授 (90016022)
Project Period (FY) 1987 – 1988
Keywordscomplex analysis / complex manifold / potential theory / Riemann surface / several complex variables / holomorphic function / hyperbolic manifold / 正則関数
Research Abstract

There are a number of outstanding results obtained under the present project and thus the aim of the project is thought to be fulfilled. One of those results is due to H.Fujimoto: He finally solved the so-called Gauss map conjecture (1961). It asserts that there are at most 4 exceptional values of the Gauss map of a complete non-fiat minimal surface in the real 3-dimensional euclidean space. He received the 1988 Geometry Prize (Japan Math. Soc.) for this work. It has been a big problem to extend a L^2 holomorphic function defined on a submanifold of a stein manifold to the whole space as L^2 holmorphic functions. T.Ohsawa solved this problem even with norm estimate. He also obtained an isomorphism theorem between the intersection and the L^2 cohomologies, and moreover established the Hodge theory on pseudoconvex Kahler manifolds (with I. Takegoshi). J.Noguchi proved the extension-convergence theorem for sequences of holomorphic mappings into a hyperbolic space anded it to obtain precise structure theorems of the moduli spaces of holomorphic mappings the results have application to the diophantus geometry over function fields and answer a few problems posed by S.Lang and other. T.Murai deepened the sutdy of analytic capacity, and solved the Vitushkin conhecture in the joint work with P.Jones. Based on works of Fricke and Weil, K.Saito found a new method to construct the Teichmuller space, which carries a canonical structure of S^1-bundle and ample group theoretical structure. It is hoped the researchs of the present project will be more actively studied and develop.

  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] Fujimoto,Hirotaka: J.Math.Soc.Japan. 108. 235-247 (1988)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ohsawa,Takano: Publ. RIMS. 24. 265-275 (1988)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Noguchi,Juhjiro: Invent, Math.93. 15-34 (1988)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Murai,Takafumi: Pacific J. Math.132. 1-16 (1987)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Imayoshi,Yoichi: Proc., Holomorphic Functions and Moduli II (Springer-Verlag). 207-219 (1988)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Saito,Kyoji: to appear.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Murai, Takafumi: "A Real Variable Method for Cauchy Tranform, and Analytic Capacity." Springer-Verlag., 133 (1988)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Akahori, Takao: "A New Approach to the Local Embedding Theorem of CR-Structures of nZ4(the Local Solvability for He Operator Ob in the scnse of the Abstract Sense)" Amer. Math. Soc., XV+257 (1987)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Fujimoto, Hirotaka.: "On the number of exceptional values of the Gauss map of minimal surfaces" J. Math. Soc. Japan. 108. 235-247 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ohsawa, Takeo.: "On the extension of L^2 holomorphic functions II" Publ. RIMS, Kyoto Univ.24. 265-275 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Noguchi, Junjiro.: "Moduli spaces of hololomorphic mappings into hyperbolically imbedded complex spaces and locally symmetric spaces" Invent. Math.93. 15-34 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Murai, Takafumi.: "Positive analitic capacity but Buffon needle probability zero" Pacific J. Math.132. 1-16 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Imayoshi, Yoichi.: "A finiteness theorem for holomorphic families of Riemann surfaces" Holomorphic Functions and Moduli II. 207-219 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Murai, Takafumi.: A Real Variable Method for the Cauchy Transform, and Analytic Capacity. Springer-Verlag, 133 (1307)

    • Description
      「研究成果報告書概要(欧文)」より

URL: 

Published: 1990-03-20  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi