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New Development of Singularity Theory

Research Project

Project/Area Number 17K05245
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionYokohama National University

Principal Investigator

NISHIMURA Takashi  横浜国立大学, 大学院環境情報研究院, 教授 (80189307)

Project Period (FY) 2017-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Keywordsウルフ図形 / フロンタル / 距離二乗写像 / 持ち上げ可能ベクトル場 / 特異点 / 可微分写像 / 球面双対変換, / isometry, / 球面ウルフ図形, / ウルフ図形, / Kato's chaos, / orthotomic, / anti-orthotomic, / フロンタル. / 球面双対変換 / ヤコビアン二乗関数芽 / 一般化された距離二乗写像 / Lowerable vector field / Convex integrand / 安定写像 / convex integrand
Outline of Final Research Achievements

I studied topics in each of the following five projects. Although three fiscal years was a relatively short period, I succeeded to obtain the result of publishing as many as 12 peer-reviewed papers during the research period of this study. Moreover, since eight of the above 12 papers are international co-authored papers, I can say that the original purpose of this study "To develop Singularities Theory in a new way with an emphasis on international joint research" was achieved.
(1) Studies on Wulff shapes and related topics from the viewpoint of Singularity theory. (2) Studies on distance-squared mappings and related topics. (3) Studies on liftable vector fields and related topics. (4) Studies on special mappings derived from Singularity Theory from the viepoint of Chaos Theory. (5) Studies on applications of frontal.

Academic Significance and Societal Importance of the Research Achievements

上記の五つの研究プロジェクトのうち「(1)ウルフ図形とその周辺の特異点論的研究」と「(2)距離二乗写像とその周辺」のプロジェクトは,世界的にみても同様の研究が見当たらない状況の中で注目を集めつつあり,十分な学術的意義がある,と言える.
また,「(5)フロンタルの応用の研究」はフロンタルの新しい研究方向を切り開くものであり,表面科学等に新しい知見を与えるとともに,数学以外の分野にフロンタルの重要性を知らしめることとなった意義を持つ.
尚,いずれの研究プロジェクトにおいても,既存の特異点論には存在しない観点からの研究が実践されており,特異点論の有用性を拡大した意義もある.

Report

(4 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (31 results)

All 2020 2019 2018 2017 Other

All Int'l Joint Research (6 results) Journal Article (12 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 10 results,  Open Access: 12 results) Presentation (10 results) (of which Int'l Joint Research: 6 results,  Invited: 1 results) Remarks (3 results)

  • [Int'l Joint Research] 西北農林科技大学(中国)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] ワルシャワ工科大学/ポーランド科学アカデミー(ポーランド)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] サンパウロ大学サンカルロス校(ブラジル)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] バレンシア大学(スペイン)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] 西北農林科技大学(中国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Cariri University(ブラジル)

    • Related Report
      2017 Research-status Report
  • [Journal Article] Kato's chaos created by quadratic mappings associated with spherical orthotomic curves2020

    • Author(s)
      Takashi Nishimura
    • Journal Title

      Journal of Singularities

      Volume: 21 Pages: 205-211

    • DOI

      10.5427/jsing.2020.21l

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Anti-orthotomics of frontals and their applications2020

    • Author(s)
      Stanislaw Janeczko and Takashi Nishimura
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 487 Issue: 2 Pages: 124019-124019

    • DOI

      10.1016/j.jmaa.2020.124019

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] The spherical dual transform is an isometry for spherical Wulff shapes2019

    • Author(s)
      Huhe Han and Takashi Nishimura
    • Journal Title

      Studia Mathematica

      Volume: 245 Issue: 3 Pages: 201-211

    • DOI

      10.4064/sm8406-9-2016

    • Related Report
      2019 Annual Research Report 2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Jacobian-squared function-germs2018

    • Author(s)
      Takashi Nishimura
    • Journal Title

      Pure and Applied Mathematics Quarterly

      Volume: 13 Issue: 4 Pages: 711-728

    • DOI

      10.4310/pamq.2017.v13.n4.a5

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Spherical method for studying Wulff shapes and related topics2018

    • Author(s)
      Huhe Han and Takashi Nishimura
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 78 Pages: 1-53

    • DOI

      10.2969/aspm/07810001

    • NAID

      120006539324

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] 可微分 convex integrand とその dual の同時安定性について2018

    • Author(s)
      西村 尚史
    • Journal Title

      RIMS kokyuroku

      Volume: 2085 Pages: 15-19

    • Related Report
      2018 Research-status Report
    • Open Access
  • [Journal Article] Preservation of immersed or injective properties by composing generic generalized distance-squared mappings2018

    • Author(s)
      Shunsuke Ichiki and Takashi Nishimura
    • Journal Title

      Springer Proceedings in Mathematics & Statistids

      Volume: 222 Pages: 537-547

    • DOI

      10.1007/978-3-319-73639-6_18

    • ISBN
      9783319736389, 9783319736396
    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Lowerable vector fields for a finitely L-determined multigerm2018

    • Author(s)
      Yusuke Mizota and Takashi Nishimura
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 47 Issue: 1 Pages: 17-23

    • DOI

      10.14492/hokmj/1520928058

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Strictly convex Wulff shapes and C^1 convex integrands2017

    • Author(s)
      Huhe Han and Takashi Nishimura
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 145 Issue: 9 Pages: 3997-4008

    • DOI

      10.1090/proc/13510

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Self-dual Wulff shapes and spherical convex bodies of constant width π/22017

    • Author(s)
      Huhe Han and Takashi Nishimura
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 69 Issue: 4 Pages: 1475-1484

    • DOI

      10.2969/jmsj/06941475

    • NAID

      130006887107

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] STABILITY OF <i>C</i><b><sup>∞ </sup></b>CONVEX INTEGRANDS2017

    • Author(s)
      Erica Boizan Batista, Huhe Han and Takashi Nishimura
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 71 Issue: 1 Pages: 187-196

    • DOI

      10.2206/kyushujm.71.187

    • NAID

      130005666252

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Wulff shapes and their duals2017

    • Author(s)
      Huhe Han and Takashi Nishimura
    • Journal Title

      RIMS Kokyuroku

      Volume: 2049 Pages: 39-44

    • Related Report
      2017 Research-status Report
    • Open Access
  • [Presentation] Jacobian-squared function-germs2019

    • Author(s)
      Takashi Nishimura
    • Organizer
      西北農林科技大学特別学術報告
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Anti-Orthotomics of Frontals2019

    • Author(s)
      Takashi Nishimura
    • Organizer
      トポロジープロジェクト研究集会【特異点論による空間研究】
    • Related Report
      2019 Annual Research Report
  • [Presentation] Anti-Orthotomics of Frontals and their Applications2019

    • Author(s)
      Takashi Nishimura
    • Organizer
      SingularityTheory Group Seminar at Sao Paulo University
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Anti-Orthotomics of Frontals and their Applications2019

    • Author(s)
      Takashi Nishimura
    • Organizer
      6th International Workshop on Singularities in Generic Geometry and its Applications, Valencia University
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Jacobian-squared function-germs2019

    • Author(s)
      Takashi Nishimura
    • Organizer
      Special Session on Real and Complex Singularities Spring Central and Western Joint Sectional Meeting, American Mathematical Society
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Projections of S^n2018

    • Author(s)
      西村 尚史
    • Organizer
      研究集会【微分幾何学・微分式系・特異点論の応用】
    • Related Report
      2018 Research-status Report
  • [Presentation] 2.Limit of the Hausdorff distance for one-parameter families of some Wulff shapes2018

    • Author(s)
      Takashi Nishimura
    • Organizer
      RIMS共同研究(公開型)【可微分写像の特異点論を用いたトポロジー・微分幾何学の研究】
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Self-dual Wulff shapes and spherical convex bodies of constant width π/22017

    • Author(s)
      Takashi Nishimura
    • Organizer
      Banach Center Conference (Bedrewo, Poland)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Simultaneous stability of C^∞ convex integrands and their duals2017

    • Author(s)
      Takashi Nishimura
    • Organizer
      RIMS研究集会
    • Related Report
      2017 Research-status Report
  • [Presentation] Stability of C^∞ convex integrands2017

    • Author(s)
      Erica Boizan Batista, Huhe Han and Takashi Nishimura
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2017 Research-status Report
  • [Remarks] 研究代表者の個人webページにおける論文リスト

    • URL

      http://www.ne.jp/asahi/nishimura/takashi/paper.html

    • Related Report
      2019 Annual Research Report
  • [Remarks] 研究代表者の個人webページにおける講演リスト

    • URL

      http://www.ne.jp/asahi/nishimura/takashi/talk.html

    • Related Report
      2019 Annual Research Report
  • [Remarks] 研究代表者の所属機関の研究者総覧

    • URL

      https://er-web.ynu.ac.jp/html/NISHIMURA_Takashi/ja.html

    • Related Report
      2019 Annual Research Report

URL: 

Published: 2017-04-28   Modified: 2021-02-19  

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