Spacelike CMC 1 surfaces with elliptic ends in de Sitter 3-Space
Abstract
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.
Cite
@article{arxiv.math/0408036,
title = {Spacelike CMC 1 surfaces with elliptic ends in de Sitter 3-Space},
author = {Shoichi Fujimori},
journal= {arXiv preprint arXiv:math/0408036},
year = {2007}
}
Comments
23 pages, 6 figures. v2: Section 3 added to give a criterion for embeddedness of elliptic ends. Corollary 5.8 added to show the existence of uncountably many CMC 1 faces from CMC 1 immersions in [MU]. New references added. v3: revision according to the referee's suggestions