Bending the helicoid

Mathematische Annalen

Volumn 339, Issue 4, 2007, Pages 783-798

  Meeks III, William H ^a   Weber, Matthias ^b  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

^b INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34748920081     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00208-007-0120-4     Document Type: Article

References (14)

1. Colding T.H. and Minicozzi W.P. (2004). The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; locally simply-connected. Ann. Math. 160: 573-615
2. Dierkes U., Hildebrandt S., Küster A. and Wohlrab O. (1992). Minimal Surfaces I. Grundlehren der mathematischen Wissenschaften 296. Springer, Heidelberg
3. Ekholm T., White B. and Wienholtz D. (2002). Embeddedness of minimal surfaces with total curvature at most -4π. Ann. Math. 155: 209-234
4. Meeks W.H. (1981). The classification of complete minimal surfaces with total curvature greater than -8π. Duke Math. J. 48: 523-535
5. Meeks W.H. (2004). The regularity of the singular set in the Colding and Minicozzi lamination theorem. Duke Math. J. 123(2): 329-334
6. Meeks W.H. (2005). The lamination metric for a Colding-Minicozzi minimal lamination. Ill. J. Math. 49: 645-658
7. Meeks, W.H. III, Pérez, J., Ros, A.: Embedded minimal surfaces: removable singularities, local pictures and parking garage structures, the dynamics of dilation invariant collections and the characterization of examples of quadratic curvature decay (preprint)
8. Meeks, W.H. III, Pérez, J., Ros, A.: The geometry of minimal surfaces of finite genus III; bounds on the topology and index of classical minimal surfaces (preprint)
9. Pérez J., Ros A. and Meeks W.H. (2004). The geometry of minimal surfaces of finite genus I; curvature estimates and quasiperiodicity. J. Differ. Geometry 66: 1-45
10. Pérez J., Ros A. and Meeks W.H. (2004). The geometry of minimal surfaces of finite genus II; nonexistence of one limit end examples. Invent. Math. 158: 323-341
11. Meeks, W.H. III, Rosenberg, H.: The minimal lamination closure theorem. Duke Math. J. (to appear)
12. Meeks, W.H. III, Rosenberg, H.: The theory of minimal surfaces in M × ℝ. Comment. Math. Helv. (to appear)
13. Rosenberg H. and Meeks W.H. (2005). The uniqueness of the helicoid and the asymptotic geometry of properly embedded minimal surfaces with finite topology. Ann. Math. 161: 727-758
14. Schoen, R.: Estimates for stable minimal surfaces in three dimensional manifolds. In: Annals of Math. Studies, vol. 103. Princeton University Press, Princeton (1983). MR0795231, Zbl 532.53042