Singularities of maximal surfaces

Shoichi Fujimori, Kentaro Saji, Masaaki Umehara, Kotaro Yamada

Research output: Contribution to journalArticlepeer-review

72 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)827-848
Number of pages22
JournalMathematische Zeitschrift
Issue number4
Publication statusPublished - Aug 2008


  • Cuspidal cross cap
  • De Sitter space
  • Maximal surfaces
  • Minkowski space

ASJC Scopus subject areas

  • Mathematics(all)


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