Singularities of maximal surfaces

被引：95

作者：

Fujimori, Shoichi ^{[4
]}

Saji, Kentaro ^{[3
]}

Umehara, Masaaki ^{[2
]}

Yamada, Kotaro ^{[1
]}

机构：

[1] Kyushu Univ, Fac Math, Higashi Ku, Fukuoka 8128581, Japan

[2] Osaka Univ, Grad Sch Sci, Dept Math, Osaka 5600043, Japan

[3] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan

[4] Fukuoka Univ Educ, Dept Math, Fukuoka 8114192, Japan

来源：

MATHEMATISCHE ZEITSCHRIFT | 2008年 / 259卷 / 04期

基金：

日本学术振兴会;

关键词：

maximal surfaces; Minkowski space; de Sitter space; cuspidal cross cap;

D O I：

10.1007/s00209-007-0250-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：827 / 848

页数：22

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