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

2004/08/03 by Shoichi Fujimori, Fujimori, Shoichi · 1 citation
Mathematics · #53A10 #53B30 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A10 #msc:53B30

paper · pdf · doi:10.48550/arxiv.math/0408036

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

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.

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