Genus-One Helicoids from a Variational Point of View

Details Genus-One Helicoids from a Variational Point of View Genus-One Helicoids from a Variational Point of View

2006-10-20

arxiv.org/abs/math/0610630v3

Comment. Math. Helv. 83 (2008), no. 4, 767-813

Mathematics

Differential Geometry

36 pages, 5 figures. Revised version: typos corrected, references added, proof of Thm 6.1 made more self-contained, several pa

Scientific paper

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.

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