The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains

Annals of Mathematics

Volumn 160, Issue 2, 2004, Pages 523-572

  Colding, Tobias H ^a,b   Minicozzi II, William P ^c  

^a NEW YORK UNIVERSITY   (United States)

^b PRINCETON UNIVERSITY   (United States)

^c JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 15944399783     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2004.160.523     Document Type: Article

References (21)

1. [CM1] T. H. COLDING and W. P. MINICOZZI II, Minimal Surfaces, Courant Lecture Notes in Math. 4, New York University Press, Courant Institute of Math. Sciences, New York (1999).
2. [CM2] _, Estimates for parametric elliptic integrands, Internat. Math. Res. Not. 6 (2002), 291-297.
3. [CMS] _, The space of embedded minimal surfaces of fixed genus in a 3-manifold I; Estimates off the axis for disks, Ann. of Math. 160 (2004), 27-68; math.AP/0210106.
4. [CM4] T. H. COLDING and W. P. MINICOZZI II, The space of embedded minimal surfaces of fixed genus in a 3-manifold II; Multi-valued graphs in disks, Ann. of Math. 160 (2004), 69-92; math.AP/0210086.
5. [CM5] _, The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected, Ann. of Math. 160 (2004), 573-615; math.AP/0210119.
6. [CM6] _, The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus, in preparation.
7. [CM7] _, Minimal annuli with and without slits, J. Symplectic Geom. 1 (2001), 47-61.
8. [CM8] _, Multi-valued minimal graphs and properness of disks, Internat. Math. Res. Not. 21 (2002), 1111-1127.
9. [CM9] _, On the structure of embedded minimal annuli, Internat. Math. Res. Not. 29 (2002), 1539-1552.
10. 3, Duke Math. J. 107 (2001), 421-126.
11. [CM11] _, Embedded minimal disks, in Minimal surfaces (MSRI, 2001), Clay Mathematics Proceedings, 405-438, D. Huffman, ed., AMS, Providence, RI, 2004; math.DG/0206146.
12. [CM12] _, Disks that are double spiral staircases, Notices Amer. Math. Soc. 50 (2003), 327-339.
13. [CM13] _, Embedded minimal disks: Proper versus nonproper - global versus local, Trans. Amer. Math. Soc. 356 (2004), 283-289.
14. [Fi] D. FISCHER-COLBRIE, On complete minimal surfaces with finite Morse index in 3-manifolds, Invent. Math. 82 (1985), 121-132.
15. [PrMe] C. FROHMAN and W. H. MEEKS, The topological uniqueness of complete one-ended minimal surfaces and Heegaard surfaces in R3, J. Amer. Math. Soc. 10 (1997), 495-512.
16. [HoKrWe] D. HUFFMAN, H. KARCHBR, and F. WEI, Adding handles to the helicoid, Bull. Amer. Math. Soc. 29 (1993), 77-84.
17. [Ka] N. KAPOULEAS, On desingularizing the intersections of minimal surfaces, Proc. 4th Internat. Congress of Geometry (Thessaloniki, 1996), 34-41, GiachoudisGiapoulis, Thessaloniki, 1997.
18. [LoRo] F. LOPEZ and A. Ros, On embedded complete minimal surfaces of genus zero, J. Differential Geom. 33 (1991), 293-300.
19. [MeYal] W. MEEKS III and S.-T. YAU, The classical Plateau problem and the topology of three-dimensional manifolds. The embedding of the solution given by Douglas-Morrey and an analytic proof of Dehn's lemma, Topology 21 (1982), 409-442.
20. [MeYa2] _, The existence of embedded minimal surfaces and the problem of uniqueness, Math. Z. 179 (1982), 151-168.
21. [Sc] R. SCHOBN, Estimates for stable minimal surfaces in three-dimensional manifolds, in Seminar on Minimal Submanifolds, Ann. of Math. Studies 103, 1111-126, Princeton Univ. Press, Princeton, NJ (1983).