Triunduloids: Embedded constant mean curvature surfaces with three ends and genus zero

Details Triunduloids: Embedded constant mean curvature surfaces with three ends and genus zero Triunduloids: Embedded constant mean curvature surfaces with three ends and genus zero

2001-02-22

arxiv.org/abs/math/0102183v2

Mathematics

Differential Geometry

LaTeX, 22 pages, 2 figures (8 ps files); full version of our announcement math.DG/9903101; final version (minor revisions) to

Scientific paper

In 1841, Delaunay constructed the embedded surfaces of revolution with constant mean curvature (CMC); these unduloids have genus zero and are now known to be the only embedded CMC surfaces with two ends and finite genus. Here, we construct the complete family of embedded CMC surfaces with three ends and genus zero; they are classified using their asymptotic necksizes. We work in a class slightly more general than embedded surfaces, namely immersed surfaces which bound an immersed three-manifold, as introduced by Alexandrov.

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