Surfaces which possess Weierstrass-type representationformula and their singularities

• Project/Area Number: 21740052
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Okayama University (2010-2012); Fukuoka University of Education (2009)
• Principal Investigator: FUJIMORI Shoichi 岡山大学, 大学院・自然科学研究科, 准教授 (00452706)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 微分幾何 / ワイエルストラス型表現公式 / 特異点 / 極小曲面 / 極大曲面 / 平均曲率一定曲面 / 周期問題 / オッサーマン型不等式

Research Abstract

Properties of surfaces which possess Weierstrass-type representation formula are investigated. For minimal surfaces in Euclidean 3-space and constant mean curvature 1 surfaces in hyperbolic 3-space, higher genus examples are constructed. For spacelike maximal surfaces in Minkowski 3-space and spacelike constant mean curvature 1 surfaces in de Sitter 3-space,the behavior of singularities and ends are investigated. Moreover, zero mean curvature surfaces in Minkowski 3-space are investigated and some non-trivial embedding are constructed.

Research Products

• [Journal Article] Hyperbolic metrics on Riemann surfaces and space-like CMC-1 Surfaces in de Sitter 3-Space in "Recent Trends in Lorentzian Geometry" (2013)
  • Author(s): Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara and Kotaro Yamada
  • Journal Title: Springer Proceedings in Mathematics & Statistics Volume: 26 Pages: 1-47
  • DOI: 10.1007/978-1-4614-4897-6_1
  • ISBN: 9781461448969, 9781461448976
  • Peer Reviewed
• [Journal Article] Hyperbolic Metrics on Riemann Surfaces and Space-Like CMC-1 Surfaces in de Sitter 3-Space (2013)
  • Author(s): Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara and Kotaro Yamada
  • Journal Title: Recent Trends in Lorentzian Geometry, Springer Proceedings in Mathematics & Statistics Volume: 26 Pages: 1-47
  • Peer Reviewed
• [Journal Article] Zero mean curvature surfaces in L^3 containing a light-like line (2012)
  • Author(s): Shoichi Fujimori
  • Journal Title: Comptes Reudus de l'Academie Sciences. Serie I. Mathematique, Volume: 350 Issue: 21-22 Pages: 975-978
  • DOI: 10.1016/j.crma.2012.10.024
  • Peer Reviewed
• [Journal Article] CMC-1 trinoids in H^3 and metrics of constant curvature one… (2011)
  • Author(s): S.Fujimori, K.Yamada, et.al.
  • Journal Title: Proceedings of Japan Academy, Ser.A. Volume: 87 Issue: 8 Pages: 144-149
  • DOI: 10.3792/pjaa.87.144
  • Peer Reviewed
• [Journal Article] NONORIENTABLE MAXIMAL SURFACES IN THE LORENTZ-MINKOWSKI 3-SPACE (2010)
  • Author(s): Shoichi Fujimoriand Francisco J. Lopez
  • Journal Title: Tohoku Mathematical Journal, Second Series Volume: 62 Issue: 3 Pages: 311-328
  • DOI: 10.2748/tmj/1287148614
  • NAID: 130004713647
  • ISSN: 0040-8735, 2186-585X
  • Peer Reviewed
• [Journal Article] HIGHER-GENUS MEAN CURVATURE-ONE CATENOIDS IN HYPERBOLIC AND DE SITTER 3-SPACES (2010)
  • Author(s): Shoichi Fujimoriand Wayne Rossman
  • Journal Title: Kyushu Journal of Mathematics Volume: 64 Issue: 2 Pages: 169-180
  • DOI: 10.2206/kyushujm.64.169
  • NAID: 130000441854
  • ISSN: 1340-6116, 1883-2032
  • Peer Reviewed
• [Journal Article] Nonorientable maxinal surfaces in the Lorentz-Minkowski 3-spece (2010)
  • Author(s): Shoichi Fujimori, Francisco J.Lopez
  • Journal Title: Tohoku Mathematical Journal Volume: 62 Pages: 311-328
  • Peer Reviewed
• [Journal Article] Higher-genus mean curvature-one catenoids in hyperbolic and de Sitter 3-spaces (2010)
  • Author(s): Shoichi Fujimori, Wayne Rossman
  • Journal Title: Kyushu Journal of Mathematics Volume: 64 Pages: 169-180
  • NAID: 130000441854
  • Peer Reviewed
• [Journal Article] A construction method for triply periodic minimal surafaces (2009)
  • Author(s): Shoichi Fujimoriand Matthias Weber
  • Journal Title: OCAMI Studies Volume: 3 Pages: 79-90
  • URL: http://www.omup.jp/modules/papers/riemann/07Fujimori.pdf
  • Peer Reviewed
• [Journal Article] New maximal surfaces in Minkowski 3-space with arbitrary genus and their cousins in de Sitter 3-space (2009)
  • Author(s): Shoichi Fujimori, Wayne Rossman, Masaaki Umehara, Kotaro Yamada and Seong-Deog Yang
  • Journal Title: Results in Mathematics Volume: 56 Issue: 1-4 Pages: 41-82
  • DOI: 10.1007/s00025-009-0443-4
  • Peer Reviewed
• [Journal Article] Spacelike mean curvature one surfaces in de Sitter 3-space (2009)
  • Author(s): Shoichi Fujimori, Wayne Rossman, Masaaki Umehara, Kotaro Yamada and Seong-Deog Yang
  • Journal Title: Communications in Analysis and Geometry Volume: 17 Pages: 383-427
  • URL: http://intlpress.com/site/pub/files/_fulltext/journals/cag/2009/0017/0003/CAG-2009-0017-0003-00022894.pdf
  • Peer Reviewed
• [Journal Article] Triply periodic minimal surfaces bounded by vertical symmetry planes (2009)
  • Author(s): Shoichi Fujimori, Matthias Weber
  • Journal Title: Manuscripta Mathematica 129 Pages: 29-53
  • Peer Reviewed
• [Journal Article] Spacelike mean curvature one surfaces in de Sitter 3-space (2009)
  • Author(s): Shoiichi Fujimori, 外5名
  • Journal Title: Communications in Analysis and Geometry 17 Pages: 383-427
  • Peer Reviewed
• [Journal Article] New maximal surfaces in Minkowski 3-space with arbitrary genus and their cousins in de Sitter 3-space (2009)
  • Author(s): Shoichi Fujimori, 外5名
  • Journal Title: Results in Mathematics 56 Pages: 41-82
  • Peer Reviewed
• [Journal Article] A construction method for triply periodic minimal surfaces (2009)
  • Author(s): Shoichi Fujimori, Matthias Weber
  • Journal Title: OCAMI Studies 3 Pages: 79-90
  • Peer Reviewed
• [Presentation] Minkowski空間の3重周期的な平均曲率0埋め込みについて (2012)
  • Author(s): 藤森祥一
  • Organizer: 第59回幾何学シンポジウム
  • Place of Presentation: 九州大学
  • Year and Date: 2012-08-28
• [Presentation] Euclid空間の極小曲面とMinkowski空間の極大曲面(1), (2) (2012)
  • Author(s): 藤森祥一
  • Organizer: 幾何学阿蘇研究集会
  • Place of Presentation: 休暇村南阿蘇
• [Presentation] Minkowski空間の３重周期的な平均曲率0埋め込みについて (2012)
  • Author(s): 藤森祥一
  • Organizer: 第59回幾何学シンポジウム
  • Place of Presentation: 九州大学
  • Invited
• [Presentation] Maximal surfaces with singularities in the Lorentz-Minkowski 3-space (2011)
  • Author(s): Shoichi Fujimori
  • Organizer: he Korean Mathematical Society Fall Meeting
  • Place of Presentation: Kyunpook Notional University.
  • Year and Date: 2011-10-21
• [Presentation] Maximal surfaces with singularities in the Lorentz-Minkowski 3-space (2011)
  • Author(s): Shoichi Fujimori
  • Organizer: The Korean Mathematical Society Fall Meeting
  • Place of Presentation: Kyungpook National University(韓国)(招待講演)
  • Year and Date: 2011-10-21
• [Presentation] Maximal surfaces in Lorentz-Minkowski 3-space with arbitrary genus and their cousins in de Sitter 3-space (2011)
  • Author(s): Shoichi Fujimori
  • Organizer: Spanish-Japanese Workshop on Differential Geometry
  • Place of Presentation: Universidad de Granada.
  • Year and Date: 2011-02-14
• [Presentation] Higher genus mean curvature 1 catenoids in hyperbolic 3-space (2011)
  • Author(s): Shoichi Fujimori
  • Organizer: The Third International Workshop on Differential Geometry
  • Place of Presentation: 佐賀大学
  • Year and Date: 2011-01-18
• [Presentation] 3次元ミンコフスキー空間内の空間的極大曲面について (2010)
  • Author(s): 藤森祥一
  • Organizer: 研究集会「擬リーマン幾何学の展開III」
  • Place of Presentation: お茶の水女子大学
  • Year and Date: 2010-12-18
• [Presentation] Minkowski空間の向き付け不可能な極大曲面について (2010)
  • Author(s): 藤森祥一
  • Organizer: 第57回幾何学シンポジウム
  • Place of Presentation: 神戸大学
  • Year and Date: 2010-08-07
• [Presentation] Maximal surfaces with singularities in the Lorentz-Minkowski 3-space (2010)
  • Author(s): Shoichi Fujimori
  • Organizer: Progress in surface theory
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach.
  • Year and Date: 2010-05-04
• [Presentation] Maximal surfaces with singularities in the Lorentz-Minkowski 3-space (2010)
  • Author(s): Shoichi Fujimori
  • Organizer: Progress in surface theory
  • Place of Presentation: Mathematisches Forschungsinstitut Oherwolfach(ドイツ)
  • Year and Date: 2010-05-04
• [Presentation] 向き付け不可能な極大曲面 (2009)
  • Author(s): 藤森祥一
  • Organizer: 部分多様体論・湯沢2009
  • Place of Presentation: 湯沢グランドホテル.
  • Year and Date: 2009-11-28
• [Presentation] 3 次元Minkowski空間内の向き付け不可能な極大曲面 (2009)
  • Author(s): 藤森祥一
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学.
  • Year and Date: 2009-09-24
• [Presentation] 3次元Minkowski空間内の向き付け不可能な極大曲面 (2009)
  • Author(s): 藤森祥一
  • Organizer: 日本数学会2009年度秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-24
• [Presentation] A construction method for triply periodic minimal surfaces (2009)
  • Author(s): Shoichi Fujimori
  • Organizer: Variational problems for curves and surfaces and related topics
  • Place of Presentation: 奈良女子大学
  • Year and Date: 2009-06-30
• [Remarks]
  • URL: http://www.math.okayama-u.ac.jp/fujimori/index-j.html
• [Remarks] Shoichi Fujimori
  • URL: http://www.math.okayama-u.ac.jp/~fujimori/index-j.html
• [Remarks]
  • URL: http://www.math.okayama-u.ac.jp/~fujimori/index-j.html
• [Remarks]
  • URL: http://www.math.okayama-u.ac.jp/~fujimori/
• [Remarks]
  • URL: http://www.fue.ac.jp/~fujimori