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Mathematische Zeitschrift

, 259:827 | Cite as

Singularities of maximal surfaces

  • Shoichi Fujimori
  • Kentaro Saji
  • Masaaki Umehara
  • Kotaro Yamada
Article

Abstract

We show that the singularities of spacelike maximal surfaces in Lorentz–Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de Sitter 3-space. To prove these, we shall give a simple criterion for a given singular point on a surface to be a cuspidal cross cap.

Keywords

Maximal surfaces Minkowski space de Sitter space Cuspidal cross cap 

Mathematics Subject Classification (2000)

Primary 57R45 Secondary 53A10 53B20 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Shoichi Fujimori
    • 1
  • Kentaro Saji
    • 2
  • Masaaki Umehara
    • 3
  • Kotaro Yamada
    • 4
  1. 1.Department of MathematicsFukuoka University of EducationMunakata, FukuokaJapan
  2. 2.Department of MathematicsHokkaido UniversitySapporoJapan
  3. 3.Department of Mathematics, Graduate School of ScienceOsaka UniversityToyonaka, OsakaJapan
  4. 4.Faculty of MathematicsKyushu UniversityHigashi-ku, FukuokaJapan

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