Attaching handles to Delaunay nodoïds

Details Attaching handles to Delaunay nodoïds Attaching handles to Delaunay nodoïds

2010-10-24

arxiv.org/abs/1010.4974v1

Mathematics

Differential Geometry

Scientific paper

For all $m \in \mathbb N - \{0\}$, we prove the existence of a one dimensional family of genus $m$, constant mean curvature (equal to 1) surfaces which are complete, immersed in $\mathbb R^3$ and have two Delaunay ends asymptotic to nodo\"{\i}dal ends. Moreover, these surfaces are invariant under the group of isometries of $\mathbb R^3$ leaving a horizontal regular polygon with $m+1$ sides fixed.

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