Duke Mathematical Journal

The end behavior of complete $2$-dimensional area-minimizing $\mod 2$ surfaces in $\mathbb{R}^n$

Marty Ross
Source: Duke Math. J. Volume 63, Number 3 (1991), 623-632.
First Page: Show Hide
Primary Subjects: 53A05
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077296072
Mathematical Reviews number (MathSciNet): MR1121148
Zentralblatt MATH identifier: 0773.49021
Digital Object Identifier: doi:10.1215/S0012-7094-91-06326-X

References

[A] L. V. Ahlfors, Complex analysis: An introduction of the theory of analytic functions of one complex variable, Second edition, McGraw-Hill Book Co., New York, 1966.
Mathematical Reviews (MathSciNet): MR32:5844
Zentralblatt MATH: 0154.31904
[AG] N. L. Alling and N. Greenleaf, Foundations of the theory of Klein surfaces, Springer-Verlag, Berlin, 1971.
Mathematical Reviews (MathSciNet): MR48:11488
Zentralblatt MATH: 0225.30001
[BC] J. L. Barbosa and M. do Carmo, On the size of a stable minimal surface in $R\sp3$, Amer. J. Math. 98 (1976), no. 2, 515–528.
Mathematical Reviews (MathSciNet): MR54:1292
Zentralblatt MATH: 0332.53006
Digital Object Identifier: doi:10.2307/2373899
[CP] M. P. do Carmo and C. K. Peng, Stable complete minimal surfaces in $\bf R\sp3$ are planes, Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 6, 903–906.
Mathematical Reviews (MathSciNet): MR80j:53012
Zentralblatt MATH: 0442.53013
Digital Object Identifier: doi:10.1090/S0273-0979-1979-14689-5
Project Euclid: euclid.bams/1183544900
[F] H. Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969.
Mathematical Reviews (MathSciNet): MR41:1976
Zentralblatt MATH: 0176.00801
[FK] H. M. Farkas and I. Kra, Riemann surfaces, Graduate Texts in Mathematics, vol. 71, Springer-Verlag, New York, 1980.
Mathematical Reviews (MathSciNet): MR82c:30067
Zentralblatt MATH: 0475.30001
[FS] D. Fischer-Colbrie and R. Schoen, The structure of complete stable minimal surfaces in $3$-manifolds of nonnegative scalar curvature, Comm. Pure Appl. Math. 33 (1980), no. 2, 199–211.
Mathematical Reviews (MathSciNet): MR81i:53044
Zentralblatt MATH: 0439.53060
Digital Object Identifier: doi:10.1002/cpa.3160330206
[HO] D. A. Hoffman and R. Osserman, The geometry of the generalized Gauss map, Mem. Amer. Math. Soc. 28 (1980), no. 236, iii+105.
Mathematical Reviews (MathSciNet): MR82b:53012
Zentralblatt MATH: 0469.53004
[L] H. B. Lawson, Jr., Lectures on minimal submanifolds. Vol. I, Mathematics Lecture Series, vol. 9, Publish or Perish Inc., Wilmington, Del., 1980.
Mathematical Reviews (MathSciNet): MR82d:53035b
Zentralblatt MATH: 0434.53006
[Mi] M. J. Micallef, Stable minimal surfaces in Euclidean space, J. Differential Geom. 19 (1984), no. 1, 57–84.
Mathematical Reviews (MathSciNet): MR85e:53009
Zentralblatt MATH: 0527.32016
Project Euclid: euclid.jdg/1214438423
[Mo1] F. Morgan, Beginner's Guide To Geometry Measure Theory, Academic Press, San Diego, 1987.
[Mo2] F. Morgan, On the singular structure of two-dimensional area minimizing surfaces in $\bf R\spn$, Math. Ann. 261 (1982), no. 1, 101–110.
Mathematical Reviews (MathSciNet): MR84c:49043
Zentralblatt MATH: 0549.49029
Digital Object Identifier: doi:10.1007/BF01456413
[Mo3] F. Morgan, Harnack-type mass bounds and Bernstein theorems for area-minimizing flat chains modulo $\nu$, Comm. Partial Differential Equations 11 (1986), no. 12, 1257–1283.
Mathematical Reviews (MathSciNet): MR87m:49091
Zentralblatt MATH: 0617.49019
[Mo4] F. Morgan, Examples of unoriented area-minimizing surfaces, Trans. Amer. Math. Soc. 283 (1984), no. 1, 225–237.
Mathematical Reviews (MathSciNet): MR85b:49079
Zentralblatt MATH: 0509.53007
Digital Object Identifier: doi:10.2307/1999999
[O] R. Osserman, A survey of minimal surfaces, Dover Publications Inc., New York, 1986.
Mathematical Reviews (MathSciNet): MR87j:53012
Zentralblatt MATH: 0209.52901
[R] M. Ross, Complete minimal spheres and projective planes in $\bold R\sp n$ with simple ends, Math. Z. 201 (1989), no. 3, 375–380.
Mathematical Reviews (MathSciNet): MR90d:53014
Zentralblatt MATH: 0651.53043
Digital Object Identifier: doi:10.1007/BF01214902
[Sc] R. M. Schoen, Uniqueness, symmetry, and embeddedness of minimal surfaces, J. Differential Geom. 18 (1983), no. 4, 791–809 (1984).
Mathematical Reviews (MathSciNet): MR85f:53011
Zentralblatt MATH: 0575.53037
Project Euclid: euclid.jdg/1214438183
[Si1] L. Simon, Lectures on geometric measure theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, vol. 3, Australian National University Centre for Mathematical Analysis, Canberra, 1983.
Mathematical Reviews (MathSciNet): MR87a:49001
Zentralblatt MATH: 0546.49019
[Si2] L. Simon, Isolated singularities of extrema of geometric variational problems, Harmonic mappings and minimal immersions (Montecatini, 1984), Lecture Notes in Math., vol. 1161, Springer, Berlin, 1985, pp. 206–277.
Mathematical Reviews (MathSciNet): MR87d:58045
Zentralblatt MATH: 0583.49028
Digital Object Identifier: doi:10.1007/BFb0075139
[W] B. White, The structure of minimizing hypersurfaces mod $4$, Invent. Math. 53 (1979), no. 1, 45–58.
Mathematical Reviews (MathSciNet): MR81b:49018
Zentralblatt MATH: 0431.49044
Digital Object Identifier: doi:10.1007/BF01403190

2012 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?