Spacelike mean curvature one surfaces in de Sitter 3-space

被引：0

作者：

Fujimori, S. ^{[1
]}

Rossman, W. ^{[2
]}

Umehara, M. ^{[3
]}

Yamada, K. ^{[4
]}

Yang, S. -D. ^{[5
]}

机构：

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

[2] Kobe Univ, Fac Sci, Dept Math, Kobe, Hyogo 6578501, Japan

[3] Osaka Univ, Grad Sch Sci, Dept Math, Osaka 560043, Japan

[4] Tokyo Inst Technol, Dept Math, Meguro Ku, Tokyo 1528551, Japan

[5] Korea Univ, Dept Math, Seoul 136701, South Korea

来源：

COMMUNICATIONS IN ANALYSIS AND GEOMETRY | 2009年 / 17卷 / 03期

关键词：

CONSTANT MEAN-CURVATURE-1; HYPERSURFACES; CURVES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The first author studied spacelike constant mean curvature one (CMC-1) surfaces in the de Sitter 3-space S-1(3) when the surfaces have no singularities except within some compact subsets and are of finite total curvature on the complement of this compact subset. However, there are many CMC-1 surfaces whose singular sets are not compact. In fact, such examples have already appeared in the construction of trinoids given by Lee and the last author via hypergeometric functions. In this paper, we improve the Osserman-type inequality given by the first author. Moreover, we shall develop a fundamental framework that allows the singular set to be non-compact, and then will use it to investigate the global behavior of CMC-1 surfaces.

引用

页码：383 / 427

页数：45