@incollection{SB_1991-1992__34__463_0, 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}, series = {Ast\'erisque}, note = {talk:759}, pages = {463--535}, publisher = {Soci\'et\'e math\'ematique de France}, number = {206}, year = {1992}, mrnumber = {1206077}, zbl = {0789.53003}, language = {en}, url = {http://www.numdam.org/item/SB_1991-1992__34__463_0/} }
TY - CHAP AU - Rosenberg, Harold TI - Some recent developments in the theory of properly embedded minimal surfaces in $\mathbb {R}^3$ BT - Séminaire Bourbaki : volume 1991/92, exposés 745-759 AU - Collectif T3 - Astérisque N1 - talk:759 PY - 1992 SP - 463 EP - 535 IS - 206 PB - Société mathématique de France UR - http://www.numdam.org/item/SB_1991-1992__34__463_0/ LA - en ID - SB_1991-1992__34__463_0 ER -
%0 Book Section %A Rosenberg, Harold %T Some recent developments in the theory of properly embedded minimal surfaces in $\mathbb {R}^3$ %B Séminaire Bourbaki : volume 1991/92, exposés 745-759 %A Collectif %S Astérisque %Z talk:759 %D 1992 %P 463-535 %N 206 %I Société mathématique de France %U http://www.numdam.org/item/SB_1991-1992__34__463_0/ %G en %F 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, 73 p. http://www.numdam.org/item/SB_1991-1992__34__463_0/
[B.Do C.] On the size of a stable minimal surface in IR3. American Journal of Mathematics 98(2) : 515-528, 1976. | MR | Zbl
and .[C.-H.-M] The structure of singlyperiodic minimal surfaces. Inventiones Math. 99 : 455-481, 1990. | EuDML | MR | Zbl
, , and .[Cost.-1] Imersöes minimas en IR3 de gênero un e curvatura total finita. PhD thesis, IMPA, Rio de Janeiro, Brazil, 1982.
.[Cost.-2] Example of a complete minimal immersion in IR3 of genus one and three embedded ends. Bull. Soc. Bras. Mat. 15 : 47-54, 1984. | MR | Zbl
.[Cost.-3] Uniqueness of minimal surfaces embedded in IR3 with total curvature -12π. Journal of Differential Geometry 30(3) : 597-618, 1989. | MR | Zbl
.[Cour.] Dirichlet's Principle, Conformal Mapping and Minimal Surfaces. Interscience Publishers, Inc., New York, 1950. | MR | Zbl
.[Darb.] Leçons sur la théorie générale des surfaces et les applications géometriques du calcul infinitésimal. Gauthier-Villars, Paris, 1st part, 2nd edition, 1914. | JFM
.[Do C.-P.] Stable minimal surfaces in IR3 are planes. Bulletin of the AMS 1 : 903-906, 1979. | MR | Zbl
and .[Doug.] Solution of the problem of Plateau, Trans. AMS 33 : 263-321, 1931. | JFM | MR
,[F.-Oss.] On the Gauss curvature of non-parametric minimal surfaces, J. Anal. Math. 12 : 351-364, 1964. | MR | Zbl
and .[F.C.] On complete minimal surfaces with finite Morse index in 3-manifolds. Inventiones Math. 82 : 121-132, 1985. | MR | Zbl
.[Fr.-M.] The topological uniqueness of complete one-ended minimal surfaces and Heegard surfaces in IR3, preprint.
and .[Fuj.-1] 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 | Zbl
.[Fuj.-2] Modified defect relations for the Gauss map of minimal surfaces. Journal of Differential Geometry 29 : 245-262, 1989. | MR | Zbl
.[G.-T.] Elliptic partial differential equations of
and .second order. Springer-Verlag, New York, 2nd edition, 1983.
[H.-S.] Boundary reguarity and embedded minimal solutions for the oriented Plateau problem. Annals of Math. 110 : 439- 486, 1979. | MR | Zbl
and .[Heinz] Über die Lösungen der Minimalflächengleichung. Nachr. Akad. Wiss. Göttingen Math. Phys. K1, II (1952) 51-56. | MR | Zbl
.[H.-M.-1] A complete embedded minimal surface in IR3 with genus one and three ends. Journal of Differential Geometry 21 : 109-127, 1985. | MR | Zbl
and .[H.-M.-2] Properties of properly embedded minimal surfaces of finite total curvature. Bulletin of the AMS 17(2) : 296-300, 1987. | MR | Zbl
and .[H.-M.-3] The asymptotic behavior of properly embedded minimal surfaces of finite topology. Journal of AMS 2(4) : 667-681, 1989 | MR | Zbl
and .[H.-M.-4] The strong halfspace theorem for minimal surfaces. Inventiones Math. 101 : 373-377, 1990. | MR | Zbl
and .[H.-M.-5] Minimal surfaces based on the catenoid. Amer. Math. Monthly, Special Geometry Issue 97(8) : 702-730, 1990. | MR | Zbl
and .[H.-Wei] Adding handles to the helicoid, preprint.
and .[E.H.] On an inequality for minimal surfaces z = f(x, y), J. Rat. Mech. Anal. 2 : 519-522, 1953. | MR | Zbl
.[Hub.] On subharmonic functions and differential geometry in the large. Commentari Mathematici Helvetici 32 : 181-206, 1957. | MR | Zbl
.[J.-S.] Variational problems of minimal surface type II, Arch. Rat. Mech. Analysis 21 : 321-342, 1966. | MR | Zbl
, .[J.-Xav.] A complete minimal surface in a slab of IR3, Annals of Maths, 1980, 203-206. | MR | Zbl
, .[K.-1] 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] Embedded minimal surfaces derived from Scherk's examples. Manuscripta Math. 62 : 83-114,1988. | MR | Zbl
.[K.-3] The triply periodic minimal surfaces of Alan Schoen and
.their constant mean curvature companions. Manuscripta Math. 64 : 291- 357, 1989. | MR | Zbl
[K.-4] Construction of higher genus embedded minimal surfaces. Geom. and Top. of Sub. III World Sc. 174-191, 1990. | MR | Zbl
.[L.-R.] A maximum principle at infinity for minimal surfaces and applications. Duke Math. Journal 57 : 819-828, 1988. | MR | Zbl
and .[Lo.-Ros] On embedded complete minimal surfaces of genus zero. Journal of Differential Geometry 33(1) : 293-300, 1991. | MR | Zbl
and .[M.-1] The geometry, topology and existence of periodic minimal surfaces, preprint.
.[M.-2] Lectures on Plateau's Problem. Insituto de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, Brazil, 1978.
.[M.-3] The theory of triply-periodic minimal surfaces. Indiana University Math. Journal 39(3) : 877-936, 1990. | MR | Zbl
.[M.-R.-1] The global theory of doubly periodic minimal surfaces. Inventiones Math. 97 : 351-379, 1989. | MR | Zbl
and .[M.-R.-2] The maximum principle at infinity for minimal surfaces in flat three-manifolds. Commentari Mathematici Helvetici 65 : 255-270, 1990. | MR | Zbl
and .[M.-R.-3] The geometry and conformal structure of properly embedded minimal surfaces of finite topology in IR3, to appear in Invent. Math. | Zbl
and .[M.-R.-4] The geometry of periodic minimal surfaces, to appear in Comment. Math. Helv. | MR | Zbl
and .[M.-Wh.] Minimal surfaces bounded by convex curves in parallel planes. Commentari Mathematici Helvetici 66 : 263- 278, 1991. | MR | Zbl
and .[M.-Y.] The existence of embedded minimal surfaces and the problem of uniqueness. Math. Z. 179 : 151-168, 1982. | MR | Zbl
and .[N.] A characterization of the catenoid. Journal of Math. Mech. 11 : 293-302, 1962. | MR | Zbl
.[Oss.-1] Global properties of minimal surfaces in E3 and En. Annals of Math. 80(2) : 340-364, 1964. | MR | Zbl
.[Oss.-2] On the Gauss curvature of minimal surfaces. Trans. AMS 96 : 115-128, 1960. | MR | Zbl
.[P.-Ros] Some uniqueness and nonexistence theorems for embedded minimal surfaces, preprint. | MR
and .[Rado-1] The problem of the least area and the problem of Plateau. Math. Z. 32 : 763-796, 1930. | JFM | MR
.[Rado-2] On the problem of Plateau. Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, Berlin 1933. | JFM | MR
.[Reif.] Solution for the Plateau problem for m-dimensional surfaces of varying topological type. Acta Math. 104 : 1-92, 1960. | MR | Zbl
.[R.-T.-1] A cylindrical type complete minimal surface in a slab of IR3. Bull. Sc. Math. III, pages 241-245, 1987. | MR | Zbl
and .[R.-T.-2] Complete minimal surfaces and minimal herissons. Journal of Differential Geometry 28 : 115-132, 1988. | MR | Zbl
and .[R.-S.E.] The Dirichlet problem for the minimal surface equation on unbounded planar domains. Journal de Mathématiques Pures et Appliquées 68 : 163-183, 1989. | MR | Zbl
and .[Sch.-1] Uniqueness, symmetry, and embeddedness of minimal surfaces. Journal of Differential Geometry 18 : 791-809, 1983. | MR | Zbl
.[Sch.-2] Estimates for Stable Minimal Surfaces in Three Dimensional Manifolds, volume 103 of Annals of Math. Studies. Princeton University Press, 1983. | MR | Zbl
.[Simon] Lectures on geometric measure theory. In Proceedings of the Center for Mathematical Analysis, volume 3, Canberra, Australia, 1983. Australian National University. | MR | Zbl
.[Smale] A bridge principle for minimal and constant mean curvature submanifolds of IRn. Invent. Math. 90 : 505-549, 1987. | MR | Zbl
.[M.S.] Deformations de surfaces minimales. Thèse Univ. Paris VII, 1992.
.[Souam] Stabilité et unicité des surfaces minimales. Thèse Univ. Paris VII, 1992.
.[T.] On the uniqueness of the helicoid. Ann. Inst. Four. 38 : 121-132, 1988. | Numdam | MR | Zbl
.[Wei] Some existence and uniqueness theorems for doubly periodicminimal surfaces, to appear in Invent. Math. | MR | Zbl
.[Wh.] Complete surfaces of finite total curvature. Journ. Diff. Geom. 26 : 315-326, 1987. | MR | Zbl
.