An embedded genus-one helicoid

Matthias Weber, David Hoffman, Michael Wolf

Type: Article

Publication Date: 2009-03-01

Citations: 40

DOI: https://doi.org/10.4007/annals.2009.169.347

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.

Locations

arXiv (Cornell University) - View - PDF
Europe PMC (PubMed Central) - View - PDF
Annals of Mathematics - View - PDF

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Works Cited by This (21)

Action	Title	Year	Authors
+	Conformal Invariants: Topics in Geometric Function Theory	1973	Lars V. Ahlfors
+ PDF Chat	Projective structures with Fuchsian holonomy	1987	William M. Goldman
+	A uniqueness theorem for the singly periodic genus-one helicoid	2007	Antonio Alarcón Leonor Ferrer Francisco Martín
+	The topology of complete minimal surfaces of finite total Gaussian curvature	1983	Luquésio P. Jorge William H. Meeks
+	The geometry of periodic minimal surfaces	1993	William H. Meeks Harold Rosenberg
+ PDF Chat	The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains	2004	Tobias Colding William P. Minicozzi
+ PDF Chat	Computer graphics tools for the study of minimal surfaces	1988	Michael J. Callahan David Hoffman James T. Hoffman
+ PDF Chat	Embedded Minimal Surfaces of Finite Topology	1990	David Hoffman William H. Meeks
+ PDF Chat	Adding handles to the helicoid	1993	David Hoffman Fu Wei Hermann Karcher
+	Function theory on compact Riemann surfaces	1967	H. L. Royden