The geometry of minimal surfaces of finite genus II; nonexistence of one limit end examples

Inventiones Mathematicae

Volumn 158, Issue 2, 2004, Pages 323-341

  Meeks III, William H ^a   Pérez, Joaquín ^b   Ros, Antonio ^b  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 7544237236     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-004-0374-3     Document Type: Article

References (33)

1. Callahan, M., Hoffman, D., Meeks III, W.H.: The structure of singly-periodic minimal surfaces. Invent. Math. 99, 455-481 (1990)
2. Colding, T.H., Minicozzi II, W.P.: An excursion into geometric analysis. Surveys in Diff. Geom. IX. International Press. To appear
3. Colding, T.H., Minicozzi II, W.P.: The space of embedded minimal surfaces of fixed genus in a 3-manifold I; Estimates off the axis for disks. Ann. Math. (2). To appear. arXiv:math.AP/0210106
4. Colding, T.H., Minicozzi II, W.P.: The space of embedded minimal surfaces of fixed genus in a 3-manifold II; Multi-valued graphs in disks. Ann. Math. (2). To appear. arXiv:math.AP/0210086
5. Colding, T.H., Minicozzi II, W.P.: The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains. Ann. Math. (2). To appear. arXiv:math.AP/0210141
6. Colding, T.H., Minicozzi II, W.P.: The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply-connected. Ann. Math. (2). To appear. arXiv:math.AP/0210119
7. Colding, T.H., Minicozzi II, W.P.: The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus. In preparation
8. Colding, T.H., Minicozzi II, W.P.: Multi-valued minimal graphs and properness of disks. Int. Math. Res. Not. 21, 1111-1127 (2002)
9. 3. Ann. Math. (2) 145-1, 1-31 (1997)
10. Collin, P., Kusner, R., Meeks III, W.H., Rosenberg, H.: The geometry, conformal structure and topology of minimal surfaces with infinite topology. J. Differ. Geom. To appear
11. 3 are planes. Bull. Am. Math. Soc., New Ser. 1, 903-906 (1979)
12. Fischer-Colbrie, D.: On complete minimal surfaces with finite Morse index in 3-manifolds. Invent. Math. 82, 121-132 (1985)
13. Fischer-Colbrie, D., Schoen, R.: The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature. Commun. Pure Appl. Math. 33, 199-211 (1980)
14. Frohman, C., Meeks III, W.H.: The ordering theorem for the ends of properly embedded minimal surfaces. Topology 36, 605-617 (1997)
15. Gulliver, R., Lawson, H.B.: The structure of minimal hypersurfaces near a singularity. Proc. Symp. Pure Math. 44, 213-237 (1986)
16. Hoffman, D., Meeks III, W.H.: The strong halfspace theorem for minimal surfaces. Invent. Math. 101, 373-377 (1990)
17. López, F.J.: Minimal surfaces in a cone. Ann. Global Anal. Geom. 20, 253-299 (2001)
18. López, F.J., Ros, A.: On embedded complete minimal surfaces of genus zero. J. Differ. Geom. 33, 293-300 (1991)
19. Meeks III, W.H.: Global problems in classical minimal surface theory. Proceedings of the Clay Institute on the Global Theory of Minimal Surfaces. To appear
20. Meeks III, W.H.: The regularity of the singular set in the Colding and Minicozzi lamination theorem. Duke Math. J. To appear
21. Meeks III, W.H.: Geometric results in classical minimal surface theory. Surveys in Diff. Geom. VIII, ed. by S.T. Yau. International Press 2003
22. Meeks III, W.H., Pérez, J.: Recent advances in classical minimal surface theory. Surveys in Diff. Geom. IX. International Press. To appear
23. Meeks III, W.H., Pérez, J., Ros, A.: The geometry of minimal surfaces of finite genus I; curvature estimates and quasiperiodicity. J. Differ. Geom. To appear
24. Meeks III, W.H., Pérez, J., Ros, A.: The geometry of minimal surfaces of finite genus III; bounds on the topology and index of classical minimal surfaces. Preprint
25. Meeks III, W.H., Pérez, J., Ros, A.: The geometry of minimal surfaces of finite genus IV; Jacobi fields and uniqueness for small flux. Work in progress
26. Meeks III, W.H., Pérez, J., Ros, A.: The geometry of minimal surfaces of finite genus V; classification of genus zero examples. In preparation
27. Meeks III, W.H., Rosenberg, H.: The uniqueness of the helicoid and the asymptotic geometry of properly embedded minimal surfaces with finite topology. Ann Math. (2). To appear
28. 3. Invent. Math. 114, 625-639 (1993)
29. Pérez, J., Ros, A.: Properly embedded minimal surfaces with finite total curvature. In: The Global Theory of Minimal Surfaces in Flat Spaces Lect. Notes Math. 1775, pp. 15-66, ed. by G.P. Pirola, Springer 1999
30. Riemann, B.: Oeuvres Mathématiques de Riemann. Paris: Gauthiers-Villars 1898
31. Ros, A.: Embedded minimal surfaces: forces, topology and symmetries. Calc. Var. Partial Differ. Equ. 4, 469-496 (1996)
32. Schoen, R.: Uniqueness, symmetry, and embeddedness of minimal surfaces. J. Differ. Geom. 18, 791-809 (1983)
33. Simon, L.: Lectures on geometric measure theory. In: Proceedings of the Center for Mathematical Analysis, Vol. 3. Canberra, Australia: Australian National University 1983