Spacelike mean curvature one surfaces in de Sitter 3-space

• DOI: 10.48550/arxiv.0706.0973
• Publication Date: 2007-01-01
• Authors: Shoichi Fujimori; Wayne Rossman; Masaaki Umehara; Kotaro Yamada; Seong-Deog Yang
• Keywords: Anti-de Sitter space

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