Deforming the singly periodic genus-one helicoid

Abstract

The Weierstrass data are derived--from geometric assumptions--for a family of screw-motion-invariant minimal surfaces asymptotic to the helicoid. The period problem for these data is solved numerically and the the surfaces are approximated using adaptive mesh methods. These simulations give strong evidence that the family exists, is continuous, consists of embedded surfaces, and limits to the genus-one helicoid.