## Triunduloids

### Embedded Constant Mean Curvature Surfaces with Three Ends and Genus Zero

**Abstract:**
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.

- triund.pdf
- 22-page PDF version of the paper, with figures
- triund.tex
- LaTeX 2e source for the paper
- triund.tgz
- Gzip'ed tar archive including the files above
as well as all the figures in EPS and PDF formats (for latex and pdflatex).

Our brief 1999 announcement of this result was published in
*Proc. Natl. Acad. Sci USA* **97**:26 (Dec. 2000),
pp. 14067-14068.
The published version is available
here as a two-page PDF file.