A plateau problem at infinity for properly immersed minimal surfaces with finite total curvature

Indiana University Mathematics Journal

Volumn 50, Issue 2, 2001, Pages 847-879

  Cosín, Claudio ^a   Ros, Antonio ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040431437     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2001.50.1829     Document Type: Article

References (33)

1. A. D. ALEXANDROV, A characteristic property of spheres, Ann. Mat. Pura Appl. (4) 58 (1962), 303-315.
2. H. CHOI & R. SCHOEN, The space of minimal embeddings of a surface into a three dimensional manifold of positive Ricci curvature, Invent. Math. 81 (1985), 387-394.
3. N. EJIRI & M. KOTANI, Index and flat ends of minimal surfaces, Tokyo J. Math. 16 (1993), 37-48.
4. D. GILBARG & N.S. TRUDINGER, Elliptic Partial Differential Equations of second order, 2nd edit., Springer Verlag (1983).
5. K. GROSSE-BRAUCKMANN, R. B. KUSNER & J. M. SULLIVAN, Classification of embedded constant mean curvature surfaces with genus zero and three ends, preprint.
6. K. GROSSE-BRAUCKMANN, R. B. KUSNER & J. M. SULLIVAN , Constant mean curvature surfaces with three ends, Research Announcement.
7. L. HAUSWIRTZ, On periodic minimal surfaces with ends of type Scherk, Preprint.
8. D. HOFFMAN & H. KARCHER, Complete embedded minimal surfaces of finite total curvature, in "Geometry V", Encyclopaedia of Math. Sci. 90 (R. Osserman ed.), Springer-Verlag (1997) 5-93.
9. D. HOFFMAN & W.H. MEEKS III, Embedded minimal surfaces of finite topology, Ann. Math. 131 (1990), 1-34.
10. D. HOFFMAN & W.H. MEEKS III, The strong halfspace theorem for minimal surfaces, Invent. Math. 101 (1990), 373-377.
11. H. JENKINS & J. SERRIN, Variational problems of minimal surface type II. Boundary value problems for the minimal surface equation, Arch. Rat. Mech. Analysis 21 (1966), 321-342.
12. L. JORGE & W. H. MEEKS III, The topology of complete minimal surfaces of finite total curvature, Topology 2 (1983), 203-221.
13. N. KAPOULEAS, Complete embedded minimal surfaces of finite total curvature, J. Diff. Geom. 47 (1997), 95-169.
14. S. KATO, M. UMEHARA & K. YAMADA, An inverse problem of the flux for minimal surfaces, Indiana Univ. Math. J. 46 (1997), 529-559.
15. S. KATO, M. UMEHARA & K. YAMADA, General existence of minimal surfaces with prescribed flux, preprint.
16. S. KATO, M. UMEHARA & K. YAMADA, General existence of minimal surfaces with prescribed flux II, Topics in Complex Analysis, Differential Geometry and Mathematical Physics. World Scientific, 1997.
17. N. KOREVAAR, R. KUSNER & B. SOLOMON, The structure of complete embedded surfaces with constant mean curvature, J. Diff. Geom. 30 (1989) 465-503.
18. R. KUSNER, R. MAZZEO & D. POLLACK, The moduli space of complete embedded constant mean curvature surfaces, Geom. Funct. Anal. 6 (1996), 120-137.
19. R. MAZZEO & F. PACARD, Constant mean curvature surfaces with Delauny ends, preprint.
20. R. MAZZEO & D. POLLACK, Gluing and moduli for some noncompact geometric problems, in Geometric Theory of Singular Phenomena in Partial Differential Equations, Symposia Mathematica Vol XXXVIII, Cambridge Univ. Press (1998), 17-51.
21. W. H. MEEKS III, J. PÉREZ & A. ROS, Uniqueness of the Riemann Minimal examples, Invent. Math. 131 (1998), 107-132.
22. W. H. MEEKS III & H. ROSENBERG, The geometry of periodic minimal surfaces, Coment. Math. Helv. 68 (1993), 538-578.
23. S. MONTIEL & A. ROS, Schrödinger operators associated to a holomorphic map, Proceedings Conference on Global Differential Geometry and Global Analysis. Berlin 1990, Lecture Notes in Math. 1481 147-174.
24. R. OSSERMAN, A survey on minimal surfaces, Cambridge Univ. Press, New York (1989).
25. J. PÉREZ, On singly periodic minimal surfaces with planar ends, Trans. Amer. Math. Soc. 349 (1997), 2371-2389.
26. J. PÉREZ & A. ROS, The space of properly embedded minimal surfaces with finite total curvature, Indiana Univ. Math. J. 45 (1996), 177-204.
27. A. ROS, Compactness of space of properly embedded minimal surfaces with finite total curvature, Indiana Univ. Math. J. 44 (1995), 139-152.
28. H. ROSENBERG & R. SA-EARP, The Dirichlet problem for the minimal surface equation on unbounded planar domains, J. Math. Pures Appl. 68 (1989), 163-183.
29. R. SCHOEN, Uniqueness, Symmetry and embeddedness of minimal surfaces, J. Diff Geometry 18 (1983), 791-809.
30. M. TRAIZET, Gluing minimal surfaces with implicit function theorem, preprint.
31. M. TRAIZET, Construction of triply periodic minimal surfaces, preprint.
32. B. WHITE, Curvature estimates and compactness theorems in 3-manifolds for surfaces that are stationary for parametric elliptic functionals, Invent. Math. 88 (1987), 243-256.
33. S.D. YANG, A connected sum construction for complete minimal surfaces with finite total curvature, preprint.