New directions of research of cut locus and related topics

• Project/Area Number: 23540098
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kumamoto University
• Principal Investigator: ITOH Jin-ichi 熊本大学, 教育学部, 教授 (20193493)
• Co-Investigator(Kenkyū-buntansha): KIYOHARA Kazuyoshi 岡山大学, 理学部, 教授 (80153245)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000); Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 測地線 / 最小跡 / 共役跡 / 多面体 / 第一共役跡 / 全曲率 / 幾何学 / 第１共役跡

Research Abstract

This research was separated 5 themes and got progress all themes as the synthetic research. (A) As an extension to general dimension of Jacobi's last statement we could determine the type of its singularities. (B) A main paper of series of studies of the structure of cut locus by using graph theory was accepted. (C) The sensational paper was published which proved by using cut locus that every point on surface is a critical point of distance function from some point. (D) By using cut locus we showed any convex polyhedron is continuously flattened. (E) We construct Finslerian metric with fractal cut locus. In these studies it seems the flattening of polyhedral with cut locus structure is a remarkable new direction of research.

Research Products

• [Journal Article] The Total Absolute Torsion of Open Curves in E^3 (2014)
  • Author(s): Kazuyuki Enomoto, Jin-ichi Itoh
  • Journal Title: Illinois Journal of Mathematics Volume: in press
  • Peer Reviewed
• [Journal Article] Every graph is a cut locus (2014)
  • Author(s): Jin-ichi Itoh, Costin Vilcu
  • Journal Title: Journal of the Mathematical Society of Japan Volume: in press
  • Peer Reviewed
• [Journal Article] Transformability and Reversibility of Unfoldings of Doubly-Covered Polyhedra (2014)
  • Author(s): Jin-ichi Itoh, Chie Nara
  • Journal Title: Proceeding of JCDCG Volume: in press
  • Peer Reviewed
• [Journal Article] Affine Classes of 3-Dimensional Parallelohedra -Their Parametrization- (2014)
  • Author(s): Nikolai Dolbilin, Jin-ichi Itoh, Chie Nara
  • Journal Title: Lecture Notes in Computer Science Volume: 8296
  • Peer Reviewed
• [Journal Article] Every point is critical (2013)
  • Author(s): I. Barany, J. Itoh, C. Vilcu, T. Zamfirescu
  • Journal Title: Advances in Math Volume: 235 Pages: 390-397
  • Peer Reviewed
• [Journal Article] The total absolute curvature of open curves E^n, Proceedings of the workshop on Differential Geometry of Submanifolds and its related topics (2013)
  • Author(s): K. Enomoto, J. Itoh
  • Pages: 190-204
  • Peer Reviewed
• [Journal Article] Refold rigidity of convex polyhedra (2013)
  • Author(s): E. Demaine, M. Demaine, J. Itoh, A. Lubiw, C. Nara, J. O'Rourke
  • Journal Title: Computational Geometry Theory and Applications Volume: 46 Pages: 979-989
  • Peer Reviewed
• [Journal Article] Every point is critical (2013)
  • Author(s): I. B´ar´any, J. Itoh, C. Vilcu
  • Journal Title: Advances in Mathematics Volume: 235 Pages: 390-397
  • DOI: 10.1016/j.aim.2012.12.002
  • Peer Reviewed
• [Journal Article] The total absolute curvature of open curves E^n (2013)
  • Author(s): Kazuyuki Enomoto, Jin-ichi Itoh
  • Journal Title: Proceedings of the workshop on Differential Geometry of Submanifolds and Volume: 1 Pages: 190-204
  • Peer Reviewed
• [Journal Article] 教育学部・教育学研究科における数学の研究－２つの事例－ (2013)
  • Author(s): 伊藤仁一
  • Journal Title: 「数学教師に必要な数学能力とその育成法に関する研究」京都大学数理解析研究所講究録 Volume: 1867 Pages: 171-179
• [Journal Article] The total absolute curvature of open curves E^n (2013)
  • Author(s): Kazuyuki Enomoto, Jin-ichi Itoh
  • Journal Title: Proceedings of the workshop on Differential Geometry of Submanifolds and its Volume: in press
  • Peer Reviewed
• [Journal Article] 小学校算数科・教科専門科目の講義内容に関する現況調査の結果と標準モデルの提案 (2013)
  • Author(s): 丹羽雅彦, 松岡隆, 川﨑謙一郎, 大竹博巳, 伊藤仁一
  • Journal Title: 「数学教師に必要な数学能力に関連する諸問題」 数理解析研究所講究録 Volume: 1828 Pages: 50-60
• [Journal Article] 教育学研究科・数学教育専修のカリキュラムと入学試験に関する現況調査と今後の在り方 (2013)
  • Author(s): 伊藤仁一, 松岡隆, 川﨑謙一郎, 大竹博巳, 丹羽雅彦
  • Journal Title: 「数学教師に必要な数学能力に関連する諸問題」, 数理解析研究所講究録 Volume: 1828 Pages: 131-137
• [Journal Article] 教育シンポジュウム「教師に必要な数学能力形成に対する数学者の責任」の報告 (2013)
  • Author(s): 伊藤仁一
  • Journal Title: 「数学教師に必要な数学能力に関連する諸問題」, 数理解析研究所講究録 Volume: 1828 Pages: 143-152
• [Journal Article] Continuous Flattening of a Regular Tetrahedron with Explicit Mappings (2012)
  • Author(s): J. Itoh, C. Nara
  • Journal Title: Modelling Analysis of Information Sciences Volume: 19 Pages: 127-136
  • Peer Reviewed
• [Journal Article] Cut locus structures on graphs (2012)
  • Author(s): J. Itoh & C. Vilcu
  • Journal Title: Discrete Math Volume: 312 Pages: 524-531
  • Peer Reviewed
• [Journal Article] Continuous Flattening of Convex Polyhedra (2012)
  • Author(s): J. Itoh, C. Nara & C. Vilcu
  • Journal Title: Proc. of XIV Spanish Meeting on Computational Geometry Volume: LNCS7579 Pages: 85-97
  • Peer Reviewed
• [Journal Article] Continuous flattening of convex polyhedra (2012)
  • Author(s): Jin-ichi Itoh, Chie Nara, Costin Vilcu
  • Journal Title: Computational Geometry, LNCS Volume: 7579 Pages: 85-97
  • Peer Reviewed
• [Journal Article] 正多面体の辺による展開の再折り凸多面体―立方体を中心として― (2012)
  • Author(s): 伊藤仁一, 奈良知恵, 柴尾有星，高木淳，濱智大，山下雄太郎，山下進太朗
  • Journal Title: 熊本大学教育学部紀要 Volume: 61 Pages: 65-74
  • NAID: 110009526593
• [Journal Article] Cut locus structures on graphs (2012)
  • Author(s): J. Itoh & C. Vilcu
  • Journal Title: Discrete Math. Volume: 312 Pages: 524-531
  • Peer Reviewed
• [Journal Article] Continuous Flattening of Convex Polyhedra (2012)
  • Author(s): J. Itoh, C. Nara & C. Vilcu
  • Journal Title: accepted (Proc. of XIV Spanish Meeting on Computational Geometry) Volume: 未定
  • Peer Reviewed
• [Journal Article] 鋭角三角形分割と正四面体の通る穴 -前原先生との素晴らしい出会い- (2012)
  • Author(s): 伊藤仁一
  • Journal Title: 教育開発 Volume: 6 Pages: 45-49
• [Journal Article] Continuous flattening of platonic polyhedral (2011)
  • Author(s): J. Itoh & C. Nara
  • Journal Title: Lecture note in computer science Volume: 7033 Pages: 108-121
  • Peer Reviewed
• [Journal Article] Singular semi-classical approximation on Liouville surfaces (2011)
  • Author(s): K. Kiyohara
  • Journal Title: Differential Geom. Appl Volume: 29
  • Peer Reviewed
• [Journal Article] Cut loci and conjugate loci on Liouville surfaces (2011)
  • Author(s): J. Itoh, K. Kiyohara
  • Journal Title: manuscript math Volume: 136 Pages: 115-141
  • Peer Reviewed
• [Journal Article] Moderation of convex bodies (2011)
  • Author(s): J. Itoh, T. Zamfirescu
  • Journal Title: J. Convex Anal Volume: 18 Pages: 865-872
  • Peer Reviewed
• [Journal Article] Quasigeodesics and farthest points on convex surfaces (2011)
  • Author(s): K. Ieiri, J. Itoh & C. Vilcu
  • Journal Title: Advances in Geom Volume: 18 Pages: 571-584
  • Peer Reviewed
• [Journal Article] Cut loci and conjugate loci on Liouville surfaces (2011)
  • Author(s): J. Itoh & K. Kiyohara
  • Journal Title: Manuscripta Math. Volume: 136 Pages: 115-141
  • Peer Reviewed
• [Journal Article] Moderation of convex bodies (2011)
  • Author(s): J. Itoh & T. Zamfirescu
  • Journal Title: J. Convex Anal. Volume: 18 Pages: 865-872
  • Peer Reviewed
• [Journal Article] Quasigeodesics and farthest points on convex surfaces (2011)
  • Author(s): K. Ieiri, J. Itoh & C. Vilcu
  • Journal Title: Advances in Geom. Volume: 11 Pages: 571-584
  • Peer Reviewed
• [Journal Article] Unfoldings of doubly covered polyhedra and applications to space-fillers (2011)
  • Author(s): J. Itoh & C. Nara
  • Journal Title: Period. Math. Hungar. Volume: 63 Pages: 47-64
  • Peer Reviewed
• [Journal Article] Affine equivalent classes of parallelohedra (2011)
  • Author(s): N. Dolbilin, J. Itoh & C. Nara
  • Journal Title: Lecture note in computer science Volume: 7033 Pages: 55-60
  • Peer Reviewed
• [Journal Article] Continuous flattening of platonic polyhedra (2011)
  • Author(s): J. Itoh & C. Nara
  • Journal Title: Lecture note in computer science Volume: 7033 Pages: 108-121
  • Peer Reviewed
• [Journal Article] 四角形及び多角形への垂心のある種の拡張 (2011)
  • Author(s): 伊藤仁一， J. Buyant
  • Journal Title: 熊本大学教育学部紀要 自然科学 Volume: 60 Pages: 51-58
  • NAID: 110008750929
• [Journal Article] Singular semi-classical approximation on Liouville surfaces (2011)
  • Author(s): K. Kiyohara
  • Journal Title: Differential Geom. Appl. Volume: 29
  • Peer Reviewed
• [Journal Article] Every graph is a cut locus
  • Author(s): J. Itoh, C. Vilcu
  • Journal Title: J. Math. Soc. Japan Volume: (to appear)(受理済)
  • Peer Reviewed
• [Journal Article] The total absolute torsion of open curve in E^3
  • Author(s): K, Enomoto, J. Itoh
  • Journal Title: Illinois J. Math Volume: (to appear)(受理済)
  • Peer Reviewed
• [Journal Article] Transformability and reversibility of unfoldings of doublly-covered polyhedral
  • Author(s): J. Itoh, C. Nara
  • Journal Title: Proc. JCDCG Volume: (to appear)(受理済)
  • Peer Reviewed
• [Journal Article] Affine classes of 3-dimensional parallelhedra -their parametrization
  • Author(s): N. Dolbilin, J. Itoh, C. Nara
  • Journal Title: LNCS 8296 Volume: (to appear)(受理済)
  • Peer Reviewed
• [Presentation] Cut locus structurte (2014)
  • Author(s): 伊藤仁一
  • Organizer: 日本数学会年会
  • Place of Presentation: 学習院大学
  • Year and Date: 2014-03-16
• [Presentation] Continuous flattening of truncated tetrahedral, Mexican conf. on discrete mathematics and computational geometry (2013)
  • Author(s): C. Nara
  • Place of Presentation: Oaxaca(Mexico)
  • Year and Date: 2013-11-14
• [Presentation] Cut locus , disatance function and transformer, Geometry and something (2013)
  • Author(s): 伊藤仁一
  • Place of Presentation: 福岡大学
  • Year and Date: 2013-11-03
• [Presentation] Every graph is cut locus (2013)
  • Author(s): 伊藤仁一
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 愛媛大学
  • Year and Date: 2013-09-26
• [Presentation] Remarkes on reversibility of unfolding of doubly-covered polyhedral (2013)
  • Author(s): C. Nara
  • Organizer: JCDCGG 2013
  • Place of Presentation: 東京理科大
  • Year and Date: 2013-09-18
• [Presentation] Transversality and reversability of unfolding of doublycovered polyhedral (2013)
  • Author(s): C. Nara
  • Organizer: Conf. on Discrete Mathematics
  • Place of Presentation: Bucharest (Romania)
  • Year and Date: 2013-09-11
• [Presentation] Fractal cut locus, Conf. on Discrete Math (2013)
  • Author(s): J. Itoh
  • Organizer: Discrete Geometry and Alexandrov surfaces
  • Place of Presentation: Bucharest(Romania)
  • Year and Date: 2013-09-08
• [Presentation] Cut locus and its application (2013)
  • Author(s): J. Itoh
  • Organizer: Geometry seminar at Universitad Autonoma de Madrid
  • Place of Presentation: Madrid(Spain)
  • Year and Date: 2013-09-04
• [Presentation] 3次元凸平行多面体のアフィン同値類-媒介変数表示- (2013)
  • Author(s): 奈良知恵
  • Organizer: 日本数学会年会
  • Place of Presentation: 京都大学
  • Year and Date: 2013-03-21
• [Presentation] Refold rigidityと空間曲線の全捩率 (2013)
  • Author(s): 伊藤仁一
  • Organizer: 直観幾何学
  • Place of Presentation: 熊本大学
  • Year and Date: 2013-02-11
• [Presentation] 楕円体の共役跡の特異点について (2013)
  • Author(s): 清原一吉
  • Organizer: 測地線及び関連する諸問題
  • Place of Presentation: 熊本大学
  • Year and Date: 2013-01-14
• [Presentation] Refold reigidity of convex polyhedra と曲線の全捩率等 (2013)
  • Author(s): 伊藤仁一
  • Organizer: 測地線及び関連する諸問題
  • Place of Presentation: 熊本大学
• [Presentation] 平行多面体のアフィン同値類と準正多面体の平面折りたたみ (2013)
  • Author(s): 奈良知恵
  • Organizer: 直観幾何学
  • Place of Presentation: 熊本大学
• [Presentation] Refold rigidity と 空間曲線の全捩率 (2013)
  • Author(s): 伊藤仁一
  • Organizer: 直観幾何学
  • Place of Presentation: 熊本大学
• [Presentation] 学部生，大学院生の研究―再折凸多面体，紙で織る曲面，正十二面体の閉測地線等― (2013)
  • Author(s): 伊藤仁一
  • Organizer: 数学リテラシー概念に元ずく教員養成系数学カリキュラムの開発
  • Place of Presentation: 南九州大学(都城）
• [Presentation] Continuous flattening of polyhedra -from Platonic to Archimedean solids- (2012)
  • Author(s): Jin-ichi Itoh
  • Organizer: Tailand-Japan joint conf. on computational geometry and graphs
  • Place of Presentation: Bangkok(Thailand)
  • Year and Date: 2012-12-07
• [Presentation] 凸多面体の展開の再折り凸多面体 (2012)
  • Author(s): 伊藤仁一
  • Organizer: 部分多様体論・湯沢2012
  • Place of Presentation: 湯沢グランドホテル(新潟県)
  • Year and Date: 2012-11-23
  • Invited
• [Presentation] 曲線の全曲率 (2012)
  • Author(s): 榎本一之
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 九州大学
  • Year and Date: 2012-09-18
• [Presentation] Continuous flattening of Archimedean polyhedron (2012)
  • Author(s): Chie Nara
  • Organizer: The fourth geometry meeting dedicated to the centenary of A.D.Alexandrov
  • Place of Presentation: St. Petersburg(Russia)
  • Year and Date: 2012-08-22
• [Presentation] Closed geodesics on the regular dodecahedron (2012)
  • Author(s): Jin-ichi Itoh
  • Organizer: Discrete and Computational Geometry
  • Place of Presentation: Yaloslavl(Russia)
  • Year and Date: 2012-08-15
• [Presentation] リーマン多様体の最小跡と凸多面体の平面折り畳み (2012)
  • Author(s): 伊藤仁一
  • Organizer: 談話会(北海道大学数学教室)
  • Place of Presentation: 北海道大学
  • Year and Date: 2012-07-26
  • Invited
• [Presentation] Closed geodesics on the regular dodecahedron (2012)
  • Author(s): Jin-ichi Itoh
  • Organizer: Int. Conf. Mathematics of distances and applications
  • Place of Presentation: Varna(Bulgaria)
  • Year and Date: 2012-07-05
• [Presentation] Continuous flattening of convex polyhedral (2012)
  • Author(s): 伊藤仁一
  • Organizer: 日本数学会年会
  • Place of Presentation: 東京(東京理科大学神楽坂)
  • Year and Date: 2012-03-29
• [Presentation] Refold rigidity of convex polyhedral (2012)
  • Author(s): J. O'Rourke
  • Organizer: EuroCG 2012
  • Place of Presentation: Assisi (Italy)
  • Year and Date: 2012-03-21
  • Invited
• [Presentation] Cut locus and several topics of Intuitive Geometry (2012)
  • Author(s): J. Itoh
  • Organizer: Seminar on computational geometry (SUNY)
  • Place of Presentation: Long Island (USA)
  • Year and Date: 2012-03-20
• [Presentation] Cut loci on ellipsoids and continuous flattening of polyhedral (2012)
  • Author(s): J. Itoh
  • Organizer: Geometry seminar (Univ. Pennsylvania)
  • Place of Presentation: Philadelphia (USA)
  • Year and Date: 2012-03-14
• [Presentation] Cut loci of Riemannian manifolds and related topics (2012)
  • Author(s): J. Itoh
  • Organizer: Geometry seminar (CUNY)
  • Place of Presentation: New York (USA)
  • Year and Date: 2012-03-13
• [Presentation] Continuous flattening of Archimedean polyhedra (2012)
  • Author(s): Chie Nara
  • Organizer: Discrete and Computational Geometry
  • Place of Presentation: Yaloslavl(Russia)
• [Presentation] Continuous flattening of Archimedean polyhedron (2012)
  • Author(s): Chie Nara
  • Organizer: The fourth geometry meeting dedicated to the centenary of A.D.Alexandrov
  • Place of Presentation: St.Petersburg(Russia)
• [Presentation] 凸多面体の展開の再折り凸多面体 (2012)
  • Author(s): 伊藤仁一
  • Organizer: 部分多様体論・湯沢2012
  • Place of Presentation: 湯沢グランドホテル(新潟県）
  • Invited
• [Presentation] 曲線の幾何学と折れ線近似 (2012)
  • Author(s): 榎本一之
  • Organizer: 部分多様体論・湯沢2012
  • Place of Presentation: 湯沢グランドホテル(新潟県）
  • Invited
• [Presentation] Affine classes of 3-dimensional parallelohedra -their parametrization and structure- (2012)
  • Author(s): Chie Nara
  • Organizer: Tailand-Japan joint conf. on computational geometry and graphs
  • Place of Presentation: Bangkok(Thailand)
• [Presentation] 角を曲がれる凸図形 ～直角とは限らない場合～ (2012)
  • Author(s): 佐藤健治
  • Organizer: 直観幾何学
  • Place of Presentation: 熊本（熊本大学）
• [Presentation] Geometry of Affine Equivalence classes of 3-dim. Parallelohedra (2012)
  • Author(s): 奈良知恵
  • Organizer: 直観幾何学
  • Place of Presentation: 熊本（熊本大学）
• [Presentation] 学部生の研究 -正多面体の unfolding の refold - (2012)
  • Author(s): 伊藤仁一
  • Organizer: 研究会「数学リテラシー概念に基づく教員養成系数学カリキュラムの開発」
  • Place of Presentation: 都城（南九州大学）
• [Presentation] Cut loci on ellipsoids and continuous flattening of polyhedra (2012)
  • Author(s): J. Itoh
  • Organizer: Geometry seminar (Univ. Pesylvania)
  • Place of Presentation: Philadelphia (USA)
• [Presentation] Cut locus and several topics of Intuitive Geometry (2012)
  • Author(s): J. Itoh
  • Organizer: Seminar on computationa geometry (SUNY)
  • Place of Presentation: Long Island (USA)
• [Presentation] Refold rigidity of convex polyhedra (2012)
  • Author(s): J. O'Rourke
  • Organizer: EuroCG 2012(招待講演)
  • Place of Presentation: Assisi (Italy)
• [Presentation] Continuous flattening of convex polyhedra (2012)
  • Author(s): 伊藤仁一
  • Organizer: 日本数学会年会
  • Place of Presentation: 東京（東京理科大学神楽坂）
• [Presentation] Moderation of convex bodies (2011)
  • Author(s): J. Itoh
  • Organizer: JCDCG 2011
  • Place of Presentation: 東京(東海大学代々木)
  • Year and Date: 2011-11-28
• [Presentation] Continuous flattening of platonic polyhedra and its applications (2011)
  • Author(s): J. Itoh
  • Organizer: Convexity, Topology, Combinatorics and Beyond
  • Place of Presentation: Puerto Vallarta (Mexico)
  • Year and Date: 2011-10-03
• [Presentation] Continuous Flattening of Convex Polyhedra (2011)
  • Author(s): C. Nara
  • Organizer: XIV Spanish Meeting on Computational Geometry
  • Place of Presentation: Alcaｌa de Henaｒes (Spain)
• [Presentation] Flat foldings of convex polyhedra (2011)
  • Author(s): C. Nara
  • Organizer: Workshop on Algebraic Combinatorics
  • Place of Presentation: Shanghai (China)
• [Presentation] 正多面体の連続的折りたたみによる平面化 II (2011)
  • Author(s): 奈良知恵
  • Organizer: 日本数学会秋期総合分科会
  • Place of Presentation: 松本（信州大学）
• [Presentation] Star unfolding convex polyhedra via quasigeodesic loops (2011)
  • Author(s): 伊藤仁一
  • Organizer: 日本数学会秋期総合分科会
  • Place of Presentation: 松本（信州大学）
• [Presentation] 凸多面体を平らに折り畳む (2011)
  • Author(s): 伊藤仁一
  • Organizer: 福岡大学幾何セミナー
  • Place of Presentation: 福岡（福岡大学）
• [Presentation] 凸多面体の連続的な折りたたみ (2011)
  • Author(s): 奈良知恵
  • Organizer: 位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜（横浜国立大学）
• [Presentation] Moderation of convex bodies (2011)
  • Author(s): J. Itoh
  • Organizer: JCDCG 2011
  • Place of Presentation: 東京（東海大学代々木）
• [Presentation] A convex example of the sofa problem (2011)
  • Author(s): K. Sato
  • Organizer: JCDCG 2011
  • Place of Presentation: 東京（東海大学代々木）
• [Presentation] 正多面体を平らに折りたたむ (2011)
  • Author(s): 伊藤仁一
  • Organizer: 数学教育の会
  • Place of Presentation: 東京（お茶の水大学）
• [Presentation] 教育学研究科における数学の研究の例 －初等幾何，円織面，紙で折る線織面等－
  • Author(s): 伊藤仁一
  • Organizer: 研究会「数学リテラシー概念に基づく教員養成系数学カリキュラムの開発」
  • Place of Presentation: 南九州大学（都城）
• [Presentation] Cut locus and its applications
  • Author(s): Jin-ichi Itoh
  • Organizer: Geometry Seminar at Universidad Autonoma de Madrid
  • Place of Presentation: Madrid (Spain)
  • Invited
• [Presentation] Fractal cut locus
  • Author(s): Jin-ichi Itoh
  • Organizer: Conference on Discrete Mathematics: Discrete geometry and Alexandrov surfaces
  • Place of Presentation: Bucharest (Romania)
  • Invited
• [Presentation] Transformavility and reversibilityof unfolding of doubly-covered polyhedra
  • Author(s): Chie Nara
  • Organizer: Conference on Discrete Mathematics: Discrete geometry and Alexandrov surfaces
  • Place of Presentation: Bucharest (Romania)
• [Presentation] Remarks on Reversibility of Unfolding of Doubly-Covered Polyhedra
  • Author(s): Chie Nara
  • Organizer: JCDCGG 2013
  • Place of Presentation: 東京理科大学
• [Presentation] Every graph is a cut locus
  • Author(s): 伊藤仁一
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 愛媛大学
• [Presentation] Continuous flattening of truncated tetrahedra
  • Author(s): Chie Nara
  • Organizer: Mexican conference on Discrete Mathematics and Computational Geometry
  • Place of Presentation: Oaxaca(Mexico)
• [Presentation] Ｃｕｔ ｌｏｃｕｓ， ｄｉｓｔａｎｃｅ ｆｕｎｃｔｉｏｎ ａｎｄ ｔｒａｎｓｆｏｒｍｅｒ
  • Author(s): 伊藤仁一
  • Organizer: Geometry and Something
  • Place of Presentation: 福岡大学
  • Invited
• [Presentation] Cut locus structure
  • Author(s): 伊藤仁一
  • Organizer: 日本数学会年会
  • Place of Presentation: 学習院大学
• [Presentation] 変形および裏返し可能性－二重被覆多面体の展開図について－
  • Author(s): 奈良知恵
  • Organizer: 日本数学会年会
  • Place of Presentation: 学習院大学
• [Presentation] リーマン多様体の最小跡と凸多面体の平面折り畳み
  • Author(s): 伊藤仁一
  • Organizer: 談話会（北海道大学数学教室）
  • Place of Presentation: 北海道大学
  • Invited
• [Presentation] Refold rigidity of convex polyhedra
  • Author(s): 奈良知恵
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 九州大学
• [Presentation] ３次元凸平行多面体のアフィン同値類―媒介変数表示―
  • Author(s): 奈良知恵
  • Organizer: 日本数学会年会
  • Place of Presentation: 京都大学