Singularities of maximal surfaces

• DOI: 10.1007/s00209-007-0250-0
• Publication Date: 2007-10-04T11:24:33Z
• Authors: Shoichi Fujimori; Kentaro Saji; Masaaki Umehara; Kotaro Yamada
• Keywords: Mathematics - Differential Geometry; Differential Geometry (math.DG); 57R45, 53A10, 53B30; FOS: Mathematics; 0101 mathematics; 01 natural sciences

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.<br/>20 pages, 2 figures<br/>