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Schoen, Richard; Simon, Leon

Regularity of stable minimal hypersurfaces. (English) Zbl 0497.49034

Commun. Pure Appl. Math. 34, 741-757 (1981).
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Cited in 7 Reviews
Cited in 145 Documents

MSC:

49Q05 Minimal surfaces and optimization
49Q15 Geometric measure and integration theory, integral and normal currents in optimization
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C20 Global Riemannian geometry, including pinching
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature

Keywords:

oriented stable minimal hypersurface in a Riemannian manifold; integral curvature estimate; approximate decomposition

Citations:

Zbl 0323.53039
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Full Text: DOI

References:

[1] Almgren, Mem. Amer. Math. Soc. 165 (1976)
[2] Theory of Varifolds, Princeton Mimeographed Notes, 1965.
[3] Allard, Ann. of Math. 95 pp 417– (1972)
[4] Frontiere orientate di misura minima, Seminario Mat., Scuola Norm. Sup. Pisa, 1961.
[5] Geometric Measure Theory, Springer-Verlag, 1969. · Zbl 0176.00801
[6] Federer, Bull. Amer. Math. Soc. 76 pp 767– (1970)
[7] Multiple Integrals in the Calculus of Variations, Springer-Verlag, 1966. · Zbl 0142.38701
[8] Michael, Comm. Pure Appl. Math. 26 pp 361– (1973)
[9] Existence and regularity of minimal surfaces on Riemannian manifolds, preprint, 1979.
[10] Protter, Trans. Amer. Math. Soc. 95 pp 81– (1960)
[11] Reifenberg, Ann. of Math. 80 pp 1– (1964)
[12] Existence and regularity theorems for some geometric variational problems, Thesis, Stanford University, 1977.
[13] Schoen, Acta Math. 134 pp 276– (1975)
[14] Simons, Ann. of Math. 2 pp 62– (1968)
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