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

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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.
LaTeX, 22 pages, 2 figures (8 ps files); full version of our announcement math.DG/9903101; final version (minor revisions) to appear in Crelle's J. reine angew. Math

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Differential Geometry, 53A10 (Primary) 58D10, 53C42 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/60995

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0102183
 http://arxiv.org/abs/math/0102183

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arXiv