For every genus g, we prove that contains complete, properly embedded, genus-g minimal surfaces whose two ends are asymptotic to helicoids of any prescribed pitch. We also show that as the radius of the tends to infinity, these examples converge smoothly to complete, properly embedded minimal surfaces in that are helicoidal at infinity. We prove that helicoidal surfaces in of every prescribed genus occur as such limits of examples in .
The research of the second author was partially supported by ANR-11-ISO1-0002. The research of the third author was supported by NSF grants DMS–1105330 and DMS 1404282.
"Helicoidal minimal surfaces of prescribed genus." Acta Math. 216 (2) 217 - 323, 2016. https://doi.org/10.1007/s11511-016-0139-z