Triunduloids

Embedded Constant Mean Curvature Surfaces with Three Ends and Genus Zero

By Karsten Grosse-Brauckmann, Robert B. Kusner, and John M. Sullivan

triunduloid

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.