Singularities of Maximal Surfaces

Details Singularities of Maximal Surfaces Singularities of Maximal Surfaces

2005-10-18

arxiv.org/abs/math/0510366v4

Mathematics

Differential Geometry

20 pages, 2 figures

Scientific paper

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.

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