Journal of Differential Geometry

On the Gauss map of an area-minimizing hypersurface

Bruce Solomon

Full-text: Open access

Article information

Source
J. Differential Geom., Volume 19, Number 1 (1984), 221-232.

Dates
First available in Project Euclid: 26 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214438429

Digital Object Identifier
doi:10.4310/jdg/1214438429

Mathematical Reviews number (MathSciNet)
MR739788

Zentralblatt MATH identifier
0548.53051

Subjects
Primary: 49F20
Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 58E12: Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]

Citation

Solomon, Bruce. On the Gauss map of an area-minimizing hypersurface. J. Differential Geom. 19 (1984), no. 1, 221--232. doi:10.4310/jdg/1214438429. https://projecteuclid.org/euclid.jdg/1214438429


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References

  • [1] F. J. Almgren, Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem, Ann. of Math. 84 (1966) 277-292.
  • [2] E. Bombieri, E. De Giorgi and E. Giusti, Minimal cones and the Bernstein problem, Invent. Math. 7 (1969) 243-268.
  • [3] E. Bombieri and E. Giusti, Harnack's inequality for elliptic differential equations on minimal surfaces, Invent. Math. 15 (1972) 24-46.
  • [4] S. S. Chern, Minimal surfaces in an Euclidean space of N dimensions, Differential and Combinatorial Topology: A Symposium in Honor of Marston Morse, Princeton University Press, Princeton, NJ, 1965.
  • [5] S. S. Chera and R. Osserman, Complete minimal surfaces in Euclidean n-space, J. Analyse Math. 19 (1967) 15-34.
  • [6] H. Federer, Geometric measure theory, Springer, Berlin, 1969.
  • [7] H. Federer, Geometric measure theory, The singular sets of area-minimizing rectifiable currents with codimension one and area-minimizing flat chains mod two with arbitrary codimension, Bull. Amer. Math. Soc. 76 (1970) 767-771.
  • [8] W. H. Fleming, On the oriented Plateau problem, Rend. Circ. Mat. Palermo (2) 11 (1962) 69-90.
  • [9] W. Y. Hsiang, New examples of minimal embeddings of S" into Sn ()-the spherical Bernstein problem for n - 4, 5, 6, Bull. Amer. Math. Soc. 7 (1982) 377-379.
  • [10] H. B. Lawson, Jr., The equivariant Plateau problem and interior regularity, Trans. Amer. Math. Soc. 173 (1972) 231-249.
  • [11] R. Osserman, Proof of a conjecture of Nirenberg, Comm. Pure Appl. Math. 12 (1959) 229-232.
  • [12] R. Osserman, Global properties of minimal surfaces in E3 and E", Ann. of Math. (2) 80 (1964) 340-364.
  • [13] J. Simons, Minimal varieties in Riemannian manifolds, Ann. of Math. 88 (1968) 62-105.
  • [14] L. Simon, Remarks on curvature estimates for minimal hypersurfaces, Duke Math. J. 43 (1976) 545-553.
  • [15] S. T. Yau, Problem section, Seminar on differential geometry, Annals of Math. Studies, No. 102, Princeton University Press, Princeton, NJ, 1982, 664-706.