The singly periodic, genus one helicoid is conjectured to be the limit of a one parameter family of doubly periodic minimal surfaces referred to as Perturbed Genus One Scherk Surfaces. Using elementary elliptic function theory, we show such surfaces exist, solving a two-dimensional period problem by perturbing a one-dimensional problem. Using flat structures associated to these minimal surfaces, we then verify the conjecture.
About ProQuest Dissertations & Theses
With nearly 4 million records, the ProQuest Dissertations & Theses (PQDT) Global database is the most comprehensive collection of dissertations and theses in the world. It is the database of record for graduate research.
PQDT Global combines content from a range of the world's premier universities - from the Ivy League to the Russell Group. Of the nearly 4 million graduate works included in the database, ProQuest offers more than 2.5 million in full text formats. Of those, over 1.7 million are available in PDF format. More than 90,000 dissertations and theses are added to the database each year.