Genus-One Helicoids from a Variational Point of View
Differential Geometry
2009-05-16 v3
Abstract
We prove by variational means the existence of a complete, properly embedded, genus-one minimal surface in R^3 that is asymptotic to a helicoid at infinity. We also prove existence of surfaces that are asymptotic to a helicoid away from the helicoid's axis, but that have infinitely many handles arranged periodically along the axis. Finally, we prove some new properties of such helicoid-like surfaces.
Cite
@article{arxiv.math/0610630,
title = {Genus-One Helicoids from a Variational Point of View},
author = {David Hoffman and Brian White},
journal= {arXiv preprint arXiv:math/0610630},
year = {2009}
}
Comments
36 pages, 5 figures. Revised version: typos corrected, references added, proof of Thm 6.1 made more self-contained, several paragraphs added to the proof of Theorem 6.2