Some recent developments in the theory of properly embedded minimal surfaces in 3
Séminaire Bourbaki : volume 1991/92, exposés 745-759, Astérisque, no. 206 (1992), Talk no. 759, p. 463-535
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     author = {Rosenberg, Harold},
     title = {Some recent developments in the theory of properly embedded minimal surfaces in $\mathbb {R}^3$},
     booktitle = {S\'eminaire Bourbaki : volume 1991/92, expos\'es 745-759},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {206},
     year = {1992},
     note = {talk:759},
     pages = {463-535},
     zbl = {0789.53003},
     mrnumber = {1206077},
     language = {en},
     url = {http://www.numdam.org/item/SB_1991-1992__34__463_0}
}
Rosenberg, Harold. Some recent developments in the theory of properly embedded minimal surfaces in $\mathbb {R}^3$, in Séminaire Bourbaki : volume 1991/92, exposés 745-759, Astérisque, no. 206 (1992), Talk no. 759, pp. 463-535. http://www.numdam.org/item/SB_1991-1992__34__463_0/

[B.Do C.] J. L. Barbosa and M. Do Carmo. On the size of a stable minimal surface in IR3. American Journal of Mathematics 98(2) : 515-528, 1976. | MR 413172 | Zbl 0332.53006

[C.-H.-M] M. Callahan, D. Hoffman, and W. H. Meeks Iii. The structure of singlyperiodic minimal surfaces. Inventiones Math. 99 : 455-481, 1990. | MR 1032877 | Zbl 0695.53005

[Cost.-1] C. Costa. Imersöes minimas en IR3 de gênero un e curvatura total finita. PhD thesis, IMPA, Rio de Janeiro, Brazil, 1982.

[Cost.-2] C. Costa. Example of a complete minimal immersion in IR3 of genus one and three embedded ends. Bull. Soc. Bras. Mat. 15 : 47-54, 1984. | MR 794728 | Zbl 0613.53002

[Cost.-3] C. Costa. Uniqueness of minimal surfaces embedded in IR3 with total curvature -12π. Journal of Differential Geometry 30(3) : 597-618, 1989. | MR 1021368 | Zbl 0696.53001

[Cour.] R. Courant. Dirichlet's Principle, Conformal Mapping and Minimal Surfaces. Interscience Publishers, Inc., New York, 1950. | MR 36317 | Zbl 0040.34603

[Darb.] G. Darboux. Leçons sur la théorie générale des surfaces et les applications géometriques du calcul infinitésimal. Gauthier-Villars, Paris, 1st part, 2nd edition, 1914. | JFM 45.0881.05

[Do C.-P.] M. Do Carmo and C. K. Peng. Stable minimal surfaces in IR3 are planes. Bulletin of the AMS 1 : 903-906, 1979. | MR 546314 | Zbl 0442.53013

[Doug.] J. Douglas, Solution of the problem of Plateau, Trans. AMS 33 : 263-321, 1931. | JFM 57.1542.03 | MR 1501590

[F.-Oss.] R. Finn and R. Osserman. On the Gauss curvature of non-parametric minimal surfaces, J. Anal. Math. 12 : 351-364, 1964. | MR 166694 | Zbl 0122.16404

[F.C.] D. Fischer-Colbrie. On complete minimal surfaces with finite Morse index in 3-manifolds. Inventiones Math. 82 : 121-132, 1985. | MR 808112 | Zbl 0573.53038

[Fr.-M.] C. Frohman and W. H. Meeks Iii. The topological uniqueness of complete one-ended minimal surfaces and Heegard surfaces in IR3, preprint.

[Fuj.-1] H. Fujimoto. On the number of exceptional values of the Gauss maps of minimal surfaces. Journal of the Math. Society of Japan 40(2) : 235-247, 1988. | MR 930599 | Zbl 0629.53011

[Fuj.-2] H. Fujimoto. Modified defect relations for the Gauss map of minimal surfaces. Journal of Differential Geometry 29 : 245-262, 1989. | MR 982173 | Zbl 0676.53005

[G.-T.] D. Gilbarg and N. S. Trudinger. Elliptic partial differential equations of

second order. Springer-Verlag, New York, 2nd edition, 1983.

[H.-S.] R. Hardt and L. Simon. Boundary reguarity and embedded minimal solutions for the oriented Plateau problem. Annals of Math. 110 : 439- 486, 1979. | MR 554379 | Zbl 0457.49029

[Heinz] E. Heinz. Über die Lösungen der Minimalflächengleichung. Nachr. Akad. Wiss. Göttingen Math. Phys. K1, II (1952) 51-56. | MR 54182 | Zbl 0048.15401

[H.-M.-1] D. Hoffman and W. H. Meeks Iii. A complete embedded minimal surface in IR3 with genus one and three ends. Journal of Differential Geometry 21 : 109-127, 1985. | MR 806705 | Zbl 0604.53002

[H.-M.-2] D. Hoffman and W. H. Meeks Iii. Properties of properly embedded minimal surfaces of finite total curvature. Bulletin of the AMS 17(2) : 296-300, 1987. | MR 903736 | Zbl 0634.53003

[H.-M.-3] D. Hoffman and W. H. Meeks Iii. The asymptotic behavior of properly embedded minimal surfaces of finite topology. Journal of AMS 2(4) : 667-681, 1989 | MR 1002088 | Zbl 0683.53005

[H.-M.-4] D. Hoffman and W. H. Meeks Iii. The strong halfspace theorem for minimal surfaces. Inventiones Math. 101 : 373-377, 1990. | MR 1062966 | Zbl 0722.53054

[H.-M.-5] D. Hoffman and W. H. Meeks Iii. Minimal surfaces based on the catenoid. Amer. Math. Monthly, Special Geometry Issue 97(8) : 702-730, 1990. | MR 1072813 | Zbl 0737.53006

[H.-Wei] D. Hoffman and F. Wei. Adding handles to the helicoid, preprint.

[E.H.] E. Hopf. On an inequality for minimal surfaces z = f(x, y), J. Rat. Mech. Anal. 2 : 519-522, 1953. | MR 55735 | Zbl 0051.12601

[Hub.] A. Huber. On subharmonic functions and differential geometry in the large. Commentari Mathematici Helvetici 32 : 181-206, 1957. | MR 94452 | Zbl 0080.15001

[J.-S.] H. Jenkins, J. Serrin. Variational problems of minimal surface type II, Arch. Rat. Mech. Analysis 21 : 321-342, 1966. | MR 190811 | Zbl 0171.08301

[J.-Xav.] L. Jorge, F. Xavier. A complete minimal surface in a slab of IR3, Annals of Maths, 1980, 203-206. | MR 584079 | Zbl 0455.53004

[K.-1] H. Karcher. Construction of minimal surfaces. Surveys in Geometry, pages 1-96, 1989. University of Tokyo, 1989, and Lecture Notes No.12, SFB256, Bonn, 1989.

[K.-2] H. Karcher. Embedded minimal surfaces derived from Scherk's examples. Manuscripta Math. 62 : 83-114,1988. | MR 958255 | Zbl 0658.53006

[K.-3] H. Karcher. The triply periodic minimal surfaces of Alan Schoen and

their constant mean curvature companions. Manuscripta Math. 64 : 291- 357, 1989. | MR 1003093 | Zbl 0687.53010

[K.-4] H. Karcher. Construction of higher genus embedded minimal surfaces. Geom. and Top. of Sub. III World Sc. 174-191, 1990. | MR 1344467 | Zbl 0737.53007

[L.-R.] R. Langevin and H. Rosenberg. A maximum principle at infinity for minimal surfaces and applications. Duke Math. Journal 57 : 819-828, 1988. | MR 975123 | Zbl 0667.49024

[Lo.-Ros] F. J. Lopez and A. Ros. On embedded complete minimal surfaces of genus zero. Journal of Differential Geometry 33(1) : 293-300, 1991. | MR 1085145 | Zbl 0719.53004

[M.-1] W. H. Meeks Iii. The geometry, topology and existence of periodic minimal surfaces, preprint.

[M.-2] W. H. Meeks Iii. Lectures on Plateau's Problem. Insituto de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, Brazil, 1978.

[M.-3] W. H. Meeks Iii. The theory of triply-periodic minimal surfaces. Indiana University Math. Journal 39(3) : 877-936, 1990. | MR 1078743 | Zbl 0721.53057

[M.-R.-1] W. H. Meeks Iii and H. Rosenberg. The global theory of doubly periodic minimal surfaces. Inventiones Math. 97 : 351-379, 1989. | MR 1001845 | Zbl 0676.53068

[M.-R.-2] W. H. Meeks Iii and H. Rosenberg. The maximum principle at infinity for minimal surfaces in flat three-manifolds. Commentari Mathematici Helvetici 65 : 255-270, 1990. | MR 1057243 | Zbl 0713.53008

[M.-R.-3] W. H. Meeks Iii and H. Rosenberg. The geometry and conformal structure of properly embedded minimal surfaces of finite topology in IR3, to appear in Invent. Math. | Zbl 0803.53007

[M.-R.-4] W. H. Meeks Iii and H. Rosenberg. The geometry of periodic minimal surfaces, to appear in Comment. Math. Helv. | MR 1241472 | Zbl 0807.53049

[M.-Wh.] W. H. Meeks Iii and B. White. Minimal surfaces bounded by convex curves in parallel planes. Commentari Mathematici Helvetici 66 : 263- 278, 1991. | MR 1107841 | Zbl 0731.53004

[M.-Y.] W. H. Meeks Iii and S. T. Yau. The existence of embedded minimal surfaces and the problem of uniqueness. Math. Z. 179 : 151-168, 1982. | MR 645492 | Zbl 0479.49026

[N.] J. C. C. Nitsche. A characterization of the catenoid. Journal of Math. Mech. 11 : 293-302, 1962. | MR 137043 | Zbl 0106.14602

[Oss.-1] R. Osserman. Global properties of minimal surfaces in E3 and En. Annals of Math. 80(2) : 340-364, 1964. | MR 179701 | Zbl 0134.38502

[Oss.-2] R. Osserman. On the Gauss curvature of minimal surfaces. Trans. AMS 96 : 115-128, 1960. | MR 121723 | Zbl 0093.34303

[P.-Ros] J. Pérez and A. Ros. Some uniqueness and nonexistence theorems for embedded minimal surfaces, preprint. | MR 1204835

[Rado-1] T. Rado. The problem of the least area and the problem of Plateau. Math. Z. 32 : 763-796, 1930. | JFM 56.0436.01 | MR 1545197

[Rado-2] T. Rado. On the problem of Plateau. Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, Berlin 1933. | JFM 59.1341.01 | MR 344979

[Reif.] R. Reifenberg. Solution for the Plateau problem for m-dimensional surfaces of varying topological type. Acta Math. 104 : 1-92, 1960. | MR 114145 | Zbl 0099.08503

[R.-T.-1] H. Rosenberg and E. Toubiana. A cylindrical type complete minimal surface in a slab of IR3. Bull. Sc. Math. III, pages 241-245, 1987. | MR 912952 | Zbl 0631.53012

[R.-T.-2] H. Rosenberg and E. Toubiana. Complete minimal surfaces and minimal herissons. Journal of Differential Geometry 28 : 115-132, 1988. | MR 950557 | Zbl 0657.53004

[R.-S.E.] Sa Earp and H. Rosenberg. The Dirichlet problem for the minimal surface equation on unbounded planar domains. Journal de Mathématiques Pures et Appliquées 68 : 163-183, 1989. | MR 1010767 | Zbl 0696.49069

[Sch.-1] R. Schoen. Uniqueness, symmetry, and embeddedness of minimal surfaces. Journal of Differential Geometry 18 : 791-809, 1983. | MR 730928 | Zbl 0575.53037

[Sch.-2] R. Schoen. Estimates for Stable Minimal Surfaces in Three Dimensional Manifolds, volume 103 of Annals of Math. Studies. Princeton University Press, 1983. | MR 795231 | Zbl 0532.53042

[Simon] L. Simon. Lectures on geometric measure theory. In Proceedings of the Center for Mathematical Analysis, volume 3, Canberra, Australia, 1983. Australian National University. | MR 756417 | Zbl 0546.49019

[Smale] N. Smale. A bridge principle for minimal and constant mean curvature submanifolds of IRn. Invent. Math. 90 : 505-549, 1987. | MR 914848 | Zbl 0637.49020

[M.S.] M. Soret. Deformations de surfaces minimales. Thèse Univ. Paris VII, 1992.

[Souam] R. Souam. Stabilité et unicité des surfaces minimales. Thèse Univ. Paris VII, 1992.

[T.] E. Toubiana. On the uniqueness of the helicoid. Ann. Inst. Four. 38 : 121-132, 1988. | Numdam | MR 978243 | Zbl 0645.53032

[Wei] F. Wei. Some existence and uniqueness theorems for doubly periodicminimal surfaces, to appear in Invent. Math. | MR 1168368 | Zbl 0773.53005

[Wh.] B. White. Complete surfaces of finite total curvature. Journ. Diff. Geom. 26 : 315-326, 1987. | MR 906393 | Zbl 0631.53007