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1990 Fiscal Year Final Research Report Summary

Potential Theory and its Applications

Research Project

Project/Area Number 01540103
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionChiba University

Principal Investigator

YOSHIDA Hidenobu  Chiba Univ. Dept. Math. Professor, 理学部, 教授 (60009280)

Co-Investigator(Kenkyū-buntansha) NAGISA Masaru  Chiba Univ. Dept. Math., Associate, 理学部, 助教授 (50189172)
SUGIYAMA Ken-ichi  Chiba Univ. Dept. Math., Associate, 理学部, 助教授 (90206441)
KOSHITANI Sigeo  Chiba Univ. Dept. Math., Associate Profes, 理学部, 助教授 (30125926)
YANAGIHARA Niro  Chiba Univ. Dept. Math., Professor, 理学部, 教授 (70009041)
TAKAGI Ryoichi  Chiba Univ. Dept. Math., Professor, 理学部, 教授 (00015562)
Project Period (FY) 1989 – 1990
Keywordsleast harmonic majorant / Dirichlet Problem / Einstein-Kahler metric / Bogomolov-Gieseker type inequality / Chern class / Sylow p-subgroup / p-block of a finite Group / 01Theorem of Phragmen-Lindelof type
Research Abstract

1. For a subharmonic function u defined on a cone or on a cylinder which is dominated on the boundary by a certain function, we generalize the classical Phragmen-Lindelof theorem by making a harmonic majorant of u and show that if u is non-negative in addition, our harmonic majorant is the least harmonic majorant. As an application, we gave a result concerning the classical Dirichlet problem on a cone or on a cylinder-with an unbounded function defined on the boundary.
2. Solving a degenerate Monge-Ampere equation, we shall construct a family of Einstein-Kahler metrics on the smooth part of minimal varieties of general type. We shall show a subsequence of this family of Einstein-Kahler metrics converges to an Einstein-Kahler metric, whose cohomology class corresponds properly to a negative constant multiple of the first Chern class of the variety. An inequality between Chern numbers for minimal varieties, so called Bogomolov-Gieseker type inequality, will be proved. We shall obtain a sufficient condition for the tangent sheave of certain varieties to be stable.
3. Isaacs and Smith gave several character-theoretic characterizations of finite p-solvable groups G with p-length one. They gave four equivalent conditions for a finite group G with a Sylow p-subgroup P. We generalized this to an arbitrary p-block B of a finite group G in our previous paper. The purpose of this note is to complement this.

  • Research Products

    (12 results)

All Other

All Publications (12 results)

  • [Publications] Ryoichi Takagi: "Notes on the LaplaceーBeltrami Operator on A Foliated Riemannian Manifold With A Bundld With A BundleーLike Metric" Nihonkai Mathematical Journal. Vol.1. 89-106 (1990)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Niro Yanagihara: "Polynomial Difference Equations which Have Meromorphic Solutions of Finite Order" Analytic Function Theory of One Complex Variable,Longman Scientific & Technical. 368-392 (1990)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hidenobu Yoshida: "Harmonic Majorization of a Subuharmonic Function On a Cone or on Cylinder" Pacific Journal of Mathematics. (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Sigeo Koshitani: "On the Kernels of Representations of Finite Groups II" Glasgow Math.J.Vol.2. 341-347 (1990)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kenーichi Sugiyama: "Einstein+Kahler Metrics on Minimal Varieties of General Type and an Inequality between Chern Numbers" Advanced Studies in Pure Mathematics 18+1,Recent Topics in Differential and Analytic Geometry. 417-443 (1990)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Masaru Nagisa: "Relative Commutant Algebras of Powers Binary Shifts on the Hyperfinite II_1 Factor" Marh.Scandinavia.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ryoichi Takagi: "Notes on the Laplace-Beltrami Operator on a Foliated Riemannian Manifold with a Bundle-Like Metric" Nihonkai Mathematical Journal. Vol. 1. 89-106 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Niro Yanagihara: "Polynomial Difference Equations which have Meromorphic Solutions of Finite Order" Analytic Function Theory of One Complex Variable, Longman Scientific & Technical. 368-392 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hidenobu Yoshida: "Harmonic Majorization of a Subharmonic Function on a Cone or on a Cylinder," Pacific Journal of Mathematics.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Shigeo Koshitani: "On the Kernels of Representations of Finite Groups" Glasgow Math. Journal. Vol. 32. 341-347 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ken-ichi Sugiyama: "Einstein-Kahler Metrics on Minimal Varieties of General Type and an Inequality between Chern Numbers" Advanced Studies in Pure Mathematics 18-1, Recent Topics in Differential and Analytic Geometry. 417-443 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Masaru Nagisa: "Relative Commutant Algebras of Powers Binary Shifts on the Hyperfinite II_1 Factor" Math. Scandinavia.

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

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Published: 1993-08-12  

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