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Probabilistic aspects of Nevanlinna theory and their applications

Research Project

Project/Area Number 18540193
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

ATSUJI Atsushi  Keio University, 経済学部, 教授 (00221044)

Co-Investigator(Kenkyū-buntansha) 田村 要造  慶應義塾大学, 理工学部, 准教授 (50171905)
鈴木 由紀  慶應義塾大学, 医学部, 講師 (30286645)
安田 公美  慶應義塾大学, 商学部, 准教授 (40284484)
相原 義弘  沼津工業高等専門学校, 教養科, 教授 (60175718)
Co-Investigator(Renkei-kenkyūsha) TAMURA Yozo  慶應義塾大学, 理工学部, 准教授 (50171905)
SUZUKI Yuki  慶應義塾大学, 医学部 (30286645)
YASUDA Kumi  慶應義塾大学, 商学部, 准教授 (40284484)
AIHARA Yoshihiro  沼津工業高等専門学校, 教養科, 教授 (60175718)
Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥2,520,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥420,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥700,000 (Direct Cost: ¥700,000)
Keywordsネヴァンリンナ理論 / 有理形関数 / 多様体上のブラウン運動 / 値分布論 / 拡散過程 / 幾何学的関数論 / ブラウン運動 / グリーン関数
Research Abstract

ネヴァンリンナ理論は、有理形関数の除外点の個数を評価するなどの有理形関数の値分布の研究に使われる基本的な理論である。古典的なネヴァンリンナ理論が確率論を使って記述できることは研究代表者などの研究により知られている。本研究は、この確率論との関係をより深く研究することにより、一般のケーラー多様体上で定義されている有理形関数に対するネヴァンリンナ型理論を構築する。さらにそれを応用して、ケーラー多様体上の有理形関数の値分布、特に除外点の個数の評価への応用を研究した。

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (40 results)

All 2008 2007 2006 Other

All Journal Article (19 results) (of which Peer Reviewed: 13 results) Presentation (21 results)

  • [Journal Article] A second main theorem of Nevanlinna theory for meromorphic functions on complex submanifolds in C^n2008

    • Author(s)
      Atsushi Atsuji
    • Journal Title

      Potential Analysis 29

      Pages: 119-138

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A second main theorem of Nevanlinna theory for meromorphic functions on complete Kahler manifolds, Jour2008

    • Author(s)
      Atsushi Atsuji
    • Journal Title

      Math. Soc. Japan 60

      Pages: 471-490

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] eficiencies of holomorphic curves in complex projective spaces2008

    • Author(s)
      Yoshihiro Aihara
    • Journal Title

      Complex Analysis and its Applications (eds. Y. Imayoshi et.al.), OCAMI Studies, Osaka Municipal Univ. Press 2

      Pages: 119-124

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On a formula on the potential operators of absorbing Levy processes in the half space, Stoch2008

    • Author(s)
      Yozo Tamura
    • Journal Title

      Proc. Appl 118

      Pages: 199-212

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A diffusion process with a random potential consisting of two self-similar processes with different indices2008

    • Author(s)
      Yuki Suzuki
    • Journal Title

      Tokyo Journal of Mathematics 31

      Pages: 511-532

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A second main theorem of Nevanlinna theory for meromorphie functions on complex submanifolds in C^n2008

    • Author(s)
      Atsushi Atsuji
    • Journal Title

      Potential Analysis 29

      Pages: 119-138

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A second main theorem of Nevanlinna theory for meromorphic functions on complete Kahler manifolds2008

    • Author(s)
      Atsushi Atsuji
    • Journal Title

      Jour. Math. Soc. Japan 60

      Pages: 471-493

    • NAID

      10024331720

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a formula on the prtential operators of absorbing Levy processes in the half space2008

    • Author(s)
      Yozo Tamura
    • Journal Title

      Stoch. Proc. Appl. 118

      Pages: 199-212

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Recurrence and transience of multi-dimensional diffusion processes in Brownian environment2007

    • Author(s)
      H. Takahashi and Y. Tamura
    • Journal Title

      統計数理研究所共同研究リポート 195

      Pages: 121-125

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] アデール環上のMarkov過程2007

    • Author(s)
      安田 公美
    • Journal Title

      慶應義塾大学商学部創立五十周年記念日吉論文集.

      Pages: 563-578

    • Related Report
      2007 Annual Research Report
  • [Journal Article] Recurrence and transience of multi-dimensional diffusion processes in Brownian environment2007

    • Author(s)
      H.Takahashi, Y.Tamura
    • Journal Title

      統計数理研究所共同研究リポート 195

      Pages: 121-125

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Semi-stable processes on local fields2006

    • Author(s)
      Kumi Yasuda
    • Journal Title

      Tohoku Mathematical Journal 58

      Pages: 419-431

    • NAID

      110004762691

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Limit theorems for a diffusion process with a one-sided Brownian potential, Jour2006

    • Author(s)
      K.Kawazu and Y.Suzuki
    • Journal Title

      Appl. Prob 43

      Pages: 997-1012

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Operator semi-selfsimilar processes and their space scaling matrices, Statist.2006

    • Author(s)
      T. Saigo and Y. Tamura
    • Journal Title

      Probab. Letters 76

      Pages: 675-681

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Operator semi-selfsimilar processes and their space scaling matrices2006

    • Author(s)
      T.Saigo, Y.Tamura
    • Journal Title

      Statist. Probab. Letters 76

      Pages: 675-681

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Limit theorems for a diffusion process with a one-sided Brownian potential2006

    • Author(s)
      Kawazu, K., Suzuki, Y
    • Journal Title

      Journal of Applied Probability 43

      Pages: 997-1012

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Semi-stable processes on local fields2006

    • Author(s)
      K.Yasuda
    • Journal Title

      Tohoku Mathematical Journal 58

      Pages: 419-431

    • NAID

      110004762691

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Estimates on the number of the omitted values by meromorphic functions, Proceedings of the 1st MSJ-SI

    • Author(s)
      Atsushi Atsuji
    • Journal Title

      Probabilistic Approach to Geometry

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On a formula on potential operators of absorbing Levy processes in the half space

    • Author(s)
      Y.Tamura, H.Tanaka
    • Journal Title

      Stochastic Processes and their Applications To appear

    • Related Report
      2006 Annual Research Report
  • [Presentation] Deficiencies of Holomorphic Curves for Linear Systems2008

    • Author(s)
      相原義弘
    • Organizer
      等角写像・値分布論合同研究集会
    • Place of Presentation
      金沢大学
    • Year and Date
      2008-11-30
    • Related Report
      2008 Final Research Report
  • [Presentation] Deficiencies of Holomorphic Curves for Hypersurfaces and Linear Systems2008

    • Author(s)
      Y. Aihara
    • Organizer
      Workshop on Complex Hyperbolic Geometry and Related Topics
    • Place of Presentation
      Fields Institute, University of Toronto, Canada
    • Year and Date
      2008-11-19
    • Related Report
      2008 Final Research Report
  • [Presentation] Diffusions and Nevanlinna theory2008

    • Author(s)
      Atsushi Atsuji
    • Organizer
      Workshop on Complex Hyperbolic Geometry and Related Topics
    • Place of Presentation
      Fields institute, University of Toronto, Canada
    • Year and Date
      2008-11-17
    • Related Report
      2008 Final Research Report
  • [Presentation] Diffusions and Nevanlinna theory2008

    • Author(s)
      Atsushi Atsuji
    • Organizer
      Workshop on Complex Hyperbolic Geometry and Related Topics
    • Place of Presentation
      Fields institute, University of Toronto
    • Year and Date
      2008-11-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] On the number of omitted values of meromorphic functions on recurrent manifolds2008

    • Author(s)
      厚地淳
    • Organizer
      確率論と幾何学
    • Place of Presentation
      お茶の水女子大学
    • Year and Date
      2008-09-15
    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Presentation] Estimates on the number of the omitted values of meromorphic functions2008

    • Author(s)
      Atsushi Atsuji
    • Organizer
      The Mathematical Society of Japan, Seasonal Institute "Probabilistic Approach to Geometry"
    • Place of Presentation
      芝蘭会館(京都大学)
    • Year and Date
      2008-08-04
    • Related Report
      2008 Final Research Report
  • [Presentation] Estimates on the number of the omitted values of meromorphic functions2008

    • Author(s)
      Atsushi Atsuji
    • Organizer
      The Mathematical Society of Japan, Sea sonal Institute“Probabilistic Approach to Geometry"
    • Place of Presentation
      芝蘭会館(京都大学)
    • Year and Date
      2008-08-04
    • Related Report
      2008 Annual Research Report
  • [Presentation] Deficiencies of holomorphic curves in projective algebraic manifolds2008

    • Author(s)
      Y. Aihara
    • Organizer
      The 16th International conference on finite and infinite dimensional complex analysis
    • Place of Presentation
      Dongguk Univ., Korea
    • Year and Date
      2008-07-29
    • Related Report
      2008 Final Research Report
  • [Presentation] 極小部分多様体上のブラウン運動と有理形関数の値分布への応用2008

    • Author(s)
      厚地淳
    • Organizer
      東京確率論セミナー
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-07-07
    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Presentation] 有理形関数の値分布とstochastic calculus2008

    • Author(s)
      厚地淳
    • Organizer
      日本数学会年会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-24
    • Related Report
      2008 Final Research Report
  • [Presentation] 有理形関数の値会布とstochastic calculus2008

    • Author(s)
      厚地 淳
    • Organizer
      日本数学会年会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] Uniqueness of the ends, Liouville property and related topics on minimal submanifolds in Euclidean spaces2007

    • Author(s)
      厚地淳
    • Organizer
      確率論と幾何学
    • Place of Presentation
      熊本大学
    • Year and Date
      2007-10-21
    • Related Report
      2008 Final Research Report
  • [Presentation] Uniqueness of the ends,Lioulville property and related topics on minimal submanifolds in Euclidean spaces2007

    • Author(s)
      厚地 淳
    • Organizer
      確率論と幾何学
    • Place of Presentation
      熊本大学
    • Year and Date
      2007-10-21
    • Related Report
      2007 Annual Research Report
  • [Presentation] Deficiencies of holomorphic curves for hypersurfaces in complex projective spaces2007

    • Author(s)
      Y. Aihara
    • Organizer
      The 15th International conference on finite and infinite dimensional complex analysis
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2007-07-31
    • Related Report
      2008 Final Research Report
  • [Presentation] Heat operator and Nevanlinna theory, and its applications2007

    • Author(s)
      厚地淳
    • Organizer
      解析幾何セミナー
    • Place of Presentation
      名古屋大学
    • Year and Date
      2007-07-26
    • Related Report
      2008 Final Research Report
  • [Presentation] Heat operator and Nevanlinna theory,and its applications2007

    • Author(s)
      厚地 淳
    • Organizer
      解析幾何セミナー
    • Place of Presentation
      名古屋大学
    • Year and Date
      2007-07-26
    • Related Report
      2007 Annual Research Report
  • [Presentation] Defect relation of holomorphic curves and linear systems2007

    • Author(s)
      Y. Aihara
    • Organizer
      Workshop on Holomorphic Mappings, Kobayashi Hyperbolicity and Diophantine Approximation
    • Place of Presentation
      東京大学
    • Year and Date
      2007-07-22
    • Related Report
      2008 Final Research Report
  • [Presentation] 熱核を用いたNevanlinna理論---Gauss mapへの試み2007

    • Author(s)
      厚地淳
    • Organizer
      複素解析幾何セミナー
    • Place of Presentation
      東京大学
    • Year and Date
      2007-05-21
    • Related Report
      2008 Final Research Report
  • [Presentation] 熱核を用いたNevanlinna理論-Gauss mapへの試み2007

    • Author(s)
      厚地 淳
    • Organizer
      複素解析幾何セミナー
    • Place of Presentation
      東京大学
    • Year and Date
      2007-05-21
    • Related Report
      2007 Annual Research Report
  • [Presentation] Nevanlinna theory for meromorphic functions on submanifolds in C^n2006

    • Author(s)
      Atsushi Atsuji
    • Organizer
      日中セミナー
    • Place of Presentation
      同済大学(中国・上海)
    • Year and Date
      2006-08-23
    • Related Report
      2008 Final Research Report
  • [Presentation] Uniqueness and deficieneies of holomorphic curves2006

    • Author(s)
      Y. Aihara
    • Organizer
      Workshop on Holomorphic Mappings and Value Distributuion Theory
    • Place of Presentation
      東京大学
    • Year and Date
      2006-07-22
    • Related Report
      2008 Final Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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