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凸曲面と凸多面体の最遠点集合と最小跡

Research Project

Project/Area Number 04F04046
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section外国
Research Field Geometry
Research InstitutionKumamoto University
Host Researcher 伊藤 仁一  熊本大学, 教育学部, 教授
Foreign Research Fellow VILCU Costin  熊本大学, 教育学部, 外国人特別研究員
COSTIN VILCU  熊本大学, 教育学部, 外国人特別研究員
Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2006: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2005: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2004: ¥700,000 (Direct Cost: ¥700,000)
Keywords凸曲面 / 最小跡 / 多面体 / 最遠点 / 測地線
Research Abstract

昨年度の後半から始めた,凸曲面で全ての測地線が自己交差しないことと,4つの合同な三角形の面からなる4面体であることとは同値なことを示そうとする研究の細かい部分の証明をつめ,現在,論文にまとめている.また,その際に使った,単純閉測地線の長さと,そこから最も離れた点までの距離との積は,曲面の面積の2倍以下となることを用いて,凸曲面におけるいろいろな不等式を示すことが出来,これに関しては,8月に論文として出版された.
一昨年度に得られた2つの結果については,1つ目の,退化した凸曲面においてのSteinhauss型の問題についての研究は,定幅凸領域の場合の性質も加えて,共同研究者のJ.Rouyer氏を8月に招聘して,論文にまとめ投稿中である.2つ目の前半部分は,昨年度に終わっており,(4辺形を用いる比較定理を作り,凸曲面における最遠点となりえる場所を特徴付ける問題に関しては,論文を仕上げて現在投稿中である.)後半部分の凸多面体の場合に曲率がπ以上の頂点は必ずどこかの点の最遠点となることについては,滑らかな曲面への拡張を加え,論文にまとめ,投稿中である.更に,そのような点が3つ以上ある場合は,その中のどれかは,直径を与える2点の一つになることを示すことも出来,滑らかな場合の設定を現在検討中である.
J.Rouyer氏を8月に招聘した際に三人で新たに,凸曲面におけるBaireカテゴリー的観点からの多くの結果のAlexandrov曲面への拡張を検討を始め,いくらかの部分的結果を得ており,今後の発展が期待される.

Report

(3 results)
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • 2004 Annual Research Report

Research Products

(16 results)

All 2006 2005 2004 Other

All Journal Article (16 results)

  • [Journal Article] On the length of simple closed quasigeodesics on convex surfaces2006

    • Author(s)
      Itoh J., Vilcu C.
    • Journal Title

      Comptes Rendus Acad.Sci.Paris 343

      Pages: 259-264

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Tightness of Graphs : Realizations with the Two-Piece-Property2006

    • Author(s)
      Itoh J., Kuhnel W
    • Journal Title

      Roumaine Mathematique Pures et Appliques 51

      Pages: 1-19

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Properties of the farthest point mapping on convex surfaces2006

    • Author(s)
      Vilcu C.
    • Journal Title

      Roumaine Mathematique Pures et Appliques 51

      Pages: 125-134

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Symmetry and the farthest point mapping on convex surfaces2006

    • Author(s)
      Vilcu C., Zamfirescu T
    • Journal Title

      Adv.Geometry 6

      Pages: 345-353

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Simplicies passing through a hole2005

    • Author(s)
      Itoh, J., Zamfirescu, T
    • Journal Title

      J.of Geometry 83

      Pages: 65-70

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Gauss-type curvatures and tubes for polyhedral surfaces2005

    • Author(s)
      Itoh, J.
    • Journal Title

      Kumamoto Math.J. 18

      Pages: 51-56

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Total curvature of noncompact piecewise Riemannian 2-polyhedra2005

    • Author(s)
      Itoh, J, Ohtsuka, F
    • Journal Title

      Tsukuba J.Math. 29

      Pages: 471-493

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On the length of the cut locus for finitely many points2005

    • Author(s)
      Itoh, J., Zamfirescu, T.
    • Journal Title

      Advanced Geometry 5

      Pages: 97-106

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Farthest points and cut loci on some degenerate convex surface2004

    • Author(s)
      Itoh, J., Vilcu, C.
    • Journal Title

      J.of Geometry 80

      Pages: 106-120

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The cut loci and the conjugate loci on ellipsoids2004

    • Author(s)
      Itoh, J., Kiyohara, K.
    • Journal Title

      Manuscripta Math. 113

      Pages: 247-264

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Tightness of Graphs : Realizations with the Two-Piece-Property

    • Author(s)
      Itoh, J, Kuhnel, W
    • Journal Title

      Roumaine Mathernatique Pures et Appliques (発表予定)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Properties of the farthest point mapping on convex surfaces

    • Author(s)
      Vilcu C.
    • Journal Title

      Roumaine Mathematique Pures et Appliques (発表予定)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Multile farthest points on Alexsandrov surfaces

    • Author(s)
      Vilcu C., Zamfirescu, T
    • Journal Title

      Adv.Geometry (発表予定)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Symmetry and the farthest Point mapping on convex surfaces

    • Author(s)
      Vilcu, C., Zamfirescu, T.
    • Journal Title

      Advanced Geometry (発表予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Simplicies passing through a hole

    • Author(s)
      Itoh, J., Zamfirescu, T.
    • Journal Title

      J.of Geometry (発表予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Gauss-type curvatures and tubes for polyhedral surfaces

    • Author(s)
      Itoh, J.
    • Journal Title

      Kumamoto Math.J. (発表予定)

    • Related Report
      2004 Annual Research Report

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Published: 2004-04-01   Modified: 2016-04-21  

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