Spacelike mean curvature one surfaces in de Sitter 3-space

S. Fujimori, W. Rossman, M. Umehara, K. Yamada, S. D. Yang

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The first author studied spacelike constant mean curvature one (CMC-1) surfaces in the de Sitter 3-space S31 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.

Original languageEnglish
Pages (from-to)383-427
Number of pages45
JournalCommunications in Analysis and Geometry
Volume17
Issue number3
DOIs
Publication statusPublished - Jul 2009

    Fingerprint

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

Cite this

Fujimori, S., Rossman, W., Umehara, M., Yamada, K., & Yang, S. D. (2009). Spacelike mean curvature one surfaces in de Sitter 3-space. Communications in Analysis and Geometry, 17(3), 383-427. https://doi.org/10.4310/CAG.2009.v17.n3.a1