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Singularities of Maximal Surfaces

Shoichi Fujimori·Kentaro Saji·Masaaki Umehara·Kotaro Yamada
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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.

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Shoichi Fujimori, Kentaro Saji, Masaaki Umehara, Kotaro Yamada. 2007-08-31. Singularities of Maximal Surfaces. https://arxiv.org/abs/math/0510366

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