Hokkaido Mathematical Journal

FUJIMORI Shoichi,

Spacelike CMC 1 surfaces with elliptic ends in de Sitter 3-space.

Hokkaido Mathematical Journal, 35 (2006) pp.289-320

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Abstract

We show that an Osserman-type inequality holds for spacelike surfaces of constant mean curvature 1 with singularities and with elliptic ends in de Sitter 3-space. An immersed end of a constant mean curvature 1 surface is an "elliptic end" if the monodromy representation at the end is diagonalizable with eigenvalues in the unit circle. We also give a necessary and sufficient condition for equality in the inequality to hold, and in the process of doing this we derive a condition for determining when elliptic ends are embedded.

MSC(Primary)53B30
MSC(Secondary)53A10
Uncontrolled Keywordsde Sitter 3-space, spacelike CMC 1 surface, admissible singularities