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

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.