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Research on variations of invariants on Riemann surfaces under pseudoconvexity

Research Project

Project/Area Number 23740098
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionFukushima University

Principal Investigator

HAMANO Sachiko  福島大学, 人間発達文化学類, 准教授 (10469588)

Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords関数論 / 多変数関数論 / 複素解析 / スタイン多様体 / ポテンシャル論 / 等角写像 / 擬凸 / リーマン面 / 変分公式 / スパン / 再生核 / 擬凸領域 / 擬凸状領域
Outline of Final Research Achievements

We showed the variation formulas of the second order for harmonic spans and Schiffer spans on Riemann surfaces with one complex parameter, and applied them to solve the simultaneous uniformization problem. As an application of this result, we proved the uniformity of holomorphic families of non-homeomorphic planar Riemann surfaces of class O_{AD}.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (34 results)

All 2015 2014 2013 2012 2011 Other

All Journal Article (8 results) (of which Peer Reviewed: 8 results) Presentation (22 results) (of which Invited: 13 results) Book (2 results) Remarks (2 results)

  • [Journal Article] Uniformity of holomorphic families of non-homeomorphic planar Riemann surfaces2014

    • Author(s)
      S. Hamano
    • Journal Title

      Ann. Polonici Math.

      Volume: 111 Issue: 2 Pages: 165-182

    • DOI

      10.4064/ap111-2-5

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniformity of holomorphic families of non-homeomorphic planar Riemann surfaces2014

    • Author(s)
      Sachiko Hamano,
    • Journal Title

      Annales Polonici Mathematici

      Volume: 印刷中

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Schiffer functions on domains in C^n2013

    • Author(s)
      Sachiko Hamano
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: 43

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] On Oka's extra-zero problem and examples2013

    • Author(s)
      M. Abe, S. Hamano and J. Noguchi
    • Journal Title

      Math. Z.

      Volume: 275 Issue: 1-2 Pages: 79-89

    • DOI

      10.1007/s00209-012-1123-8

    • Related Report
      2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Schiffer functions on domains in C^n2013

    • Author(s)
      Sachiko Hamano
    • Journal Title

      RIMS講究録 Bessatsu

      Volume: -

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] <i>C</i><sup>1</sup> subharmonicity of harmonic spans for certain discontinuously moving Riemann surfaces2013

    • Author(s)
      Sachiko Hamano
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 65 Issue: 1 Pages: 321-341

    • DOI

      10.2969/jmsj/06510321

    • NAID

      10031177282

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] C^1 subharmonicity of harmonic spans for certain discontinuously moving Riemann surfaces2012

    • Author(s)
      Sachiko Hamano
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 64

    • NAID

      10031177282

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Variation formulas for principal functions (II) Applications to variation for harmonic spans2011

    • Author(s)
      S. Hamano, F. Maitani, and H.Yamaguchi
    • Journal Title

      Nagoya Mathematical Journal

      Volume: 204 No.2

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Variations of the metric induced by the reproducing kernel for semi-exact analytic differentials2015

    • Author(s)
      Sachiko Hamano
    • Organizer
      Geometry And Its Applications Seminar on Complex Analytic Geometry
    • Place of Presentation
      Pohang University of Science and Technology (KOREA)
    • Year and Date
      2015-03-09
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 主関数の変分公式とその応用について2015

    • Author(s)
      濱野佐知子
    • Organizer
      数学物理合同特別セミナー
    • Place of Presentation
      大阪市立大学理学研究科数学研究所
    • Year and Date
      2015-02-20
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] On the reproducing kernel for the space of semi-exact analytic differentials2015

    • Author(s)
      Sachiko Hamano
    • Organizer
      リーマン面・不連続群論研究集会
    • Place of Presentation
      大阪大学中之島センター
    • Year and Date
      2015-02-16
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 円環における半完全正則微分のなす空間の再生核2014

    • Author(s)
      濱野佐知子
    • Organizer
      日本数学会2014年度季総合分科会 函数論分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25
    • Related Report
      2014 Annual Research Report
  • [Presentation] Representation on annuli of reproducing kernels for the space of semiexact analytic differentials2014

    • Author(s)
      Sachiko Hamano
    • Organizer
      ベルグマン核を巡る解析幾何の話題
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-09-08
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Variational formulas for principal functions and applications2014

    • Author(s)
      Sachiko Hamano
    • Organizer
      Hayama Symposium on Complex Analysis in Several Variables XVII
    • Place of Presentation
      Shonan-village center (JAPAN)
    • Year and Date
      2014-07-22
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Variation formulas for principal functions and application to simultaneous uniformization and reproducing kernels on Riemann surfaces2014

    • Author(s)
      Sachiko Hamano
    • Organizer
      The XVII Conference on Analytic Functions and Related Topics
    • Place of Presentation
      Institute of Mathematics and Computer Science of The State School of Higher Education in Chelm (POLAND)
    • Year and Date
      2014-07-02
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 半完全正則微分のなす空間の再生核の多変数的変動2014

    • Author(s)
      濱野佐知子
    • Organizer
      日本数学会2014年度年会 函数論分科会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Log-plurisubharmonicity of metric deformations induced by Schiffer and harmonic spans2013

    • Author(s)
      Sachiko Hamano,
    • Organizer
      Geometry And Its Applications Seminar on Complex Analytic Geometry
    • Place of Presentation
      Pohang University of Science and Technology, KOREA
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Variation of the metric induced by Schiffer and harmonic spans2013

    • Author(s)
      濱野佐知子
    • Organizer
      名古屋大学解析幾何学セミナー
    • Place of Presentation
      名古屋大学多元数理科学研究科309講義室
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 半完全正則微分のなす空間のBergman核について2013

    • Author(s)
      濱野佐知子
    • Organizer
      第5回東北複素解析セミナー
    • Place of Presentation
      東北大学情報科学研究科棟6階小講義室.
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Log-plurisubharmonicity of metric deformations induced by Schiffer spans2012

    • Author(s)
      濱野佐知子
    • Organizer
      鳥羽微分トポロジー2012
    • Place of Presentation
      鳥羽市民文化会館
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Variation for the metrics induced by Schiffer and harmonic spans2012

    • Author(s)
      濱野佐知子
    • Organizer
      RIMS meeting: Potential Theory and its Related Fields
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Schiffer span と harmonic span が導く負曲率計量の多変数的変動2012

    • Author(s)
      濱野佐知子
    • Organizer
      日本数学会2012年度数秋季総合分科会 函数論分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Log-plurisubharmonicity of metric deformations induced by Schiffer and harmonic spans2012

    • Author(s)
      濱野佐知子
    • Organizer
      多変数関数論冬セミナー2012
    • Place of Presentation
      東北大学理学部・数理科学記念館
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Schiffer span およびharmonic span による再生核の表現とその応用2012

    • Author(s)
      濱野佐知子
    • Organizer
      日本数学会 2012 年度年会函数論分科会
    • Place of Presentation
      東京理科大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Schiffer span およびharmonic span による再生核の表現とその応用2012

    • Author(s)
      濱野佐知子
    • Organizer
      リーマン面・不連続群論研究集会(招待講演)
    • Place of Presentation
      名古屋大学多元数理科学研究科
    • Related Report
      2011 Research-status Report
  • [Presentation] 再生核のSchiffer span による表現とその応用2011

    • Author(s)
      濱野佐知子
    • Organizer
      等角写像論・値分布論研究集会(招待講演)
    • Place of Presentation
      金沢大学サテライトプラザ
    • Related Report
      2011 Research-status Report
  • [Presentation] Schiffer span の複素多変数的変動について2011

    • Author(s)
      濱野佐知子
    • Organizer
      2011 年度ポテンシャル論研究集会
    • Place of Presentation
      岐阜大学教育学部
    • Related Report
      2011 Research-status Report
  • [Presentation] Variation formulas for Schiffer span2011

    • Author(s)
      濱野佐知子
    • Organizer
      玉原多変数複素解析研究集会
    • Place of Presentation
      玉原セミナーハウス
    • Related Report
      2011 Research-status Report
  • [Presentation] Log-plurisubharmonicity of metric deformations induced by Schiffer and harmonic spans

    • Author(s)
      濱野佐知子
    • Organizer
      東京大学複素解析幾何セミナー
    • Place of Presentation
      東京大学数理科学研究科
    • Related Report
      2012 Research-status Report
  • [Presentation] 主関数の変分公式とその応用

    • Author(s)
      濱野佐知子
    • Organizer
      富山大学理学部数学科談話会
    • Place of Presentation
      富山大学理学部B棟1階B121室
    • Related Report
      2012 Research-status Report
    • Invited
  • [Book] 数学セミナー2014年12月号 特集「三角函数」2014

    • Author(s)
      砂田利一, 斎藤毅, 濱野佐知子, 平松豊一, 金子昌信, 渋川元樹など
    • Total Pages
      96
    • Publisher
      日本評論社 Vol.53_no.12_638
    • Related Report
      2014 Annual Research Report
  • [Book] 数学セミナー 2013年9月号「深遠なる複素関数」2013

    • Author(s)
      川平友規, 濱野佐知子, 小森洋平, 志賀啓成, 谷口雅彦, 梅田亨, 脇克志, 高崎金久, 吉田知行, 小澤正直
    • Total Pages
      96
    • Publisher
      日本評論社 Vol.52 no.9  623
    • Related Report
      2013 Research-status Report
  • [Remarks] 福島大学個人業績データベース

    • URL

      http://kojingyoseki.adb.fukushima-u.ac.jp/top/details/59

    • Related Report
      2014 Annual Research Report
  • [Remarks] 多変数関数論冬セミナー2013

    • URL

      https://sites.google.com/site/scvwintersemi2013/

    • Related Report
      2013 Research-status Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

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