Singularities of maximal surfaces

Shoichi Fujimori, Kentaro Saji, Masaaki Umehara, Kotaro Yamada

Research output: Contribution to journalArticle

52 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)827-848
Number of pages22
JournalMathematische Zeitschrift
Volume259
Issue number4
DOIs
Publication statusPublished - Aug 1 2008

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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    Fujimori, S., Saji, K., Umehara, M., & Yamada, K. (2008). Singularities of maximal surfaces. Mathematische Zeitschrift, 259(4), 827-848. https://doi.org/10.1007/s00209-007-0250-0