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

Details Spacelike CMC 1 surfaces with elliptic ends in de Sitter 3-Space Spacelike CMC 1 surfaces with elliptic ends in de Sitter 3-Space

2004-08-03

arxiv.org/abs/math/0408036v3

Mathematics

Differential Geometry

23 pages, 6 figures. v2: Section 3 added to give a criterion for embeddedness of elliptic ends. Corollary 5.8 added to show th

Scientific paper

We show that an Osserman-type inequality holds for spacelike surfaces of constant mean curvature (CMC) 1 with singularities and with elliptic ends in de Sitter 3-space. An immersed end of a CMC 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.

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