Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(e) ISSN 0894-0347(p)

     

The asymptotic behavior of properly embedded minimal surfaces of finite topology

Author(s): David Hoffman; William H. Meeks
Journal: J. Amer. Math. Soc. 2 (1989), 667-682.
MSC: Primary 53A10; Secondary 49F10
MathSciNet review: 1002088
Retrieve article in: PDF
This article is available free of charge

References | Similar articles | Additional information

References:

[1]
M. Anderson, Curvature estimates for minimal surfaces, Ann. Sci. École Norm. Sup. 18 (1985), 89-105. MR 803196 (87e:53098)

[2]
L. Barbosa and M. do Carmo, On the size of a stable minimal surface in $             {{\mathbf{R}}^3}$, Amer. J. Math. 19 (1976), 515-528. MR 0413172 (54:1292)

[3]
M. Callahan, D. Hoffman, and W. H. Meeks III, Embedded minimal surfaces with four ends, 1989, preprint.

[4]
-, The structure of singly-periodic minimal surfaces, Invent. Math. (to appear). MR 1032877 (92a:53005)

[5]
C. Costa, Example of a complete minimal immersion in $             {{\mathbf{R}}^3}$ of genus one and three embedded ends, Bol. Soc. Brasil. Mat. 15 (1984), 47-54. MR 794728 (87c:53111)

[6]
Y. Fang and W. Meeks, Some global properties of complete minimal surfaces in $ {{\mathbf{R}}^3}$, Topology (to appear). MR 1081931 (92g:53008)

[7]
D. Fischer-Colbrie, On complete minimal surfaces with finite Morse index in $             3$-manifolds, Invent. Math. 82 (1985), 121-132. MR 808112 (87b:53090)

[8]
D. Hoffman and W. H. Meeks III, One-parameter families of embedded minimal surfaces, 1989, preprint.

[9]
-, Properly embedded minimal surfaces of finite topology, Ann. of Math. (2) (to appear). MR 2275628 (2008f:53008)

[10]
-, The strong halfspace theorem for minimal surfaces, 1987, preprint.

[11]
-, A variational approach to the existence of complete embedded minimal surfaces, Duke J. Math. 57 (1988), 877-893. MR 975126 (90c:53023)

[12]
-, A complete embedded minimal surface with genus one, three ends and finite total curvature, J. Differential Geom. 21 (1985), 109-127. MR 806705 (87d:53008)

[13]
-, Properties of properly embedded minimal surfaces of finite total curvature, Bull. Amer. Math. Soc. 17 (1987), 296-300. MR 903736 (88m:53014)

[14]
L. Jorge and W. H. Meeks III, The topology of complete minimal surfaces of finite total Gaussian curvature, Topology 22 (1983), 203-221. MR 683761 (84d:53006)

[15]
T. C. Kuo, On $ {C^\infty }$-sufficiency of sets of potential functions, Topology 8 (1969), 167-171. MR 0238338 (38:6614)

[16]
W. H. Meeks III and H. Rosenberg, The global theory of doubly-periodic minimal surfaces, Invent. Math. (to appear). MR 1001845 (90m:53017)

[17]
-, The strong maximum principle for complete minimal surfaces in flat $             3$-manifolds, 1988, preprint.

[18]
-, The geometry of periodic minimal surfaces, 1988, preprint.

[19]
W. H. Meeks III and S. T. Yau, The topological uniqueness theorem for minimal surfaces of finite type, 1987, preprint.

[20]
-, The classical Plateau problem and the topology of three-dimensional manifolds, Topology 21 (1982), 409-442. MR 670745 (84g:53016)

[21]
-, The existence of embedded minimal surfaces and the problem of uniqueness, Math. Z. 179 (1982), 151-168. MR 645492 (83j:53060)

[22]
R. Osserman, A survey of minimal surfaces, 2nd ed., Dover, New York, 1986. MR 852409 (87j:53012)

[23]
J. Pitts and H. Rubenstein, Existence of minimal surfaces of bounded topological type in three-manifolds, Proc. Centre Math. Anal. Austral. Nat. Univ., Vol. 10, Canberra, Australia, 1987.

[24]
R. Schoen, Uniqueness, symmetry, and embeddedness of minimal surfaces, J. Differential Geom. 18 (1983), 791-809. MR 730928 (85f:53011)

[25]
L. Simon, Lectures on geometric measure theory, Proc. Centre Math. Anal. Austral. Nat. Univ., Vol. 3, Canberra, Australia, 1983. MR 756417 (87a:49001)

[26]
S. Smale, An infinite dimensional version of Sards theorem, Amer. J. Math. 87 (1965), 861-866. MR 0185604 (32:3067)

[27]
B. White, New applications of mapping degree to minimal surface theory, J. Differential Geom. 29 (1989), 143-162. MR 978083 (90e:49051)

Similar Articles:

Retrieve articles in Journal of the American Mathematical Society with MSC: 53A10, 49F10

Retrieve articles in all Journals with MSC: 53A10, 49F10


Additional Information:

DOI: 10.1090/S0894-0347-1989-1002088-X
PII: S0894-0347-1989-1002088-X
Copyright of article: Copyright 1989, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia