Singularities of maximal surfaces

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 criterio...

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Bibliographic Details
Published in:	Mathematische Zeitschrift Vol. 259; no. 4; pp. 827 - 848
Main Authors:	Fujimori, Shoichi, Saji, Kentaro, Umehara, Masaaki, Yamada, Kotaro
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer-Verlag 01-08-2008
Subjects:	Mathematics Mathematics and Statistics Cuspidal cross cap 53B20 Primary 57R45 Minkowski space Secondary 53A10 Maximal surfaces de Sitter space
Online Access:	Get full text
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Summary:	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.
ISSN:	0025-5874 1432-1823
DOI:	10.1007/s00209-007-0250-0