An embedded genus-one helicoid
arXiv:math/0401080 · doi:10.1073/pnas.0508008102
Abstract
There exists a properly embedded minimal surface of genus one with one end. The end is asymptotic to the end of the helicoid. This genus one helicoid is constructed as the limit of a continuous one-parameter family of screw-motion invariant minimal surfaces--also asymptotic to the helicoid--that have genus equal to one in the quotient.
115 pages, many figures Minor exposiitonal changes and added references