Acta Mathematica

Curvature estimates for minimal hypersurfaces

R. Schoen, L. Simon, and S. T. Yau

Full-text: Open access

Note

This research was supported in part by the National Science Foundation Grant GP-35543, AFOSR Contract F-44620-72-C-0031 and Sloan Foundation Grant.

Note

This revised version was published online in November 2006 with corrections to the Cover Date.

Article information

Source
Acta Math., Volume 134 (1975), 275-288.

Dates
Received: 26 November 1974
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485889848

Digital Object Identifier
doi:10.1007/BF02392104

Mathematical Reviews number (MathSciNet)
MR423263

Zentralblatt MATH identifier
0323.53039

Rights
1975 © Almqvist & Wiksell

Citation

Schoen, R.; Simon, L.; Yau, S. T. Curvature estimates for minimal hypersurfaces. Acta Math. 134 (1975), 275--288. doi:10.1007/BF02392104. https://projecteuclid.org/euclid.acta/1485889848


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References

  • Almgren, F. J., Jr., Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem. Ann. of Math., 84 (1966), 277–292.
  • Bernstein, S., Sur un theoreme de geometrie et ses applications aux equations aux derivees partielles du type elliptique. Comm. de la Soc. Math. de Kharkov (2éme Ser.), 15 (1915–1917), 38–45.
  • Bombieri, E., De Giorgi, E. & Giusti, E., Minimal cones and the Bernstein problem. Invent. Math, 7 (1969), 243–268.
  • Chern, S. S., Minimal submanifolds in a Riemannian manifold. Mimeographed Lecture Notes, Univ. of Kansas, 1968.
  • Chern, S. S., DoCarmo, M. & Kobayashi, S. Minimal submanifolds of a sphere with second fundamental form of constant length. In Functional Analysis and Related Fields, edited by F. Browder, Springer-Verlag, Berlin, 1970.
  • De Giorgi, E., Una estensione del teorema di, Bernstein, Ann. Scuola Norm. Sup. Pisa, III, 19, (1965), 79–85.
  • Fleming, W. H., On the oriented Plateau problem, Rend. Circ. Mat., Palermo, 2 (1962), 1–22.
  • Heinz, E., Über die Lösungen der Minimalflächengleichung, Nachr. Akad. Wiss. Göttingen Math., Phys. K1 II, (1952), 51–56.
  • Hoffman, D. & Spruck, J, Sobolev inequalities on Riemannian manifolds. To appear in Comm. Pure Appl. Math.
  • Morrey, C. B., Multiple integrals in the calculus of variations. New York, Springer-Verlag, 1966.
  • Osserman, R., A survey of minimal surfaces. Van Nostrand Reinhold Math. Studies, 1969.
  • Simons, J., Minimal varieties in Reimannian manifolds, Ann. of Math., 88 (1968), 62–105.