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Singularities of maximal surfaces |
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| Authors: | Shoichi Fujimori Kentaro Saji Masaaki Umehara and Kotaro Yamada |
| Institution: | (1) Department of Mathematics, Fukuoka University of Education, Munakata, Fukuoka 811-4192, Japan;(2) Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan;(3) Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan;(4) Faculty of Mathematics, Kyushu University, Higashi-ku, Fukuoka 812-8581, Japan |
| 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. Dedicated to Yusuke Sakane on the occasion of his 60th birthday. |
| Keywords: | Maximal surfaces Minkowski space de Sitter space Cuspidal cross cap |
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