zbMATH — the first resource for mathematics

Curvature estimates for minimal hypersurfaces. (English) Zbl 0323.53039

53C40 Global submanifolds
49Q05 Minimal surfaces and optimization
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53B25 Local submanifolds
58J99 Partial differential equations on manifolds; differential operators
57R40 Embeddings in differential topology
Full Text: DOI
[1] 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. · Zbl 0146.11905 · doi:10.2307/1970520
[2] 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.
[3] Bombieri, E., De Giorgi, E. &Giusti, E., Minimal cones and the Bernstein problem.Invent. Math, 7 (1969), 243–268. · Zbl 0183.25901 · doi:10.1007/BF01404309
[4] Chern, S. S.,Minimal submanifolds in a Riemannian manifold. Mimeographed Lecture Notes, Univ. of Kansas, 1968.
[5] Chern, S. S., DoCarmo, M. &Kobayashi, S. Minimal submanifolds of a sphere with second fundamental form of constant length. InFunctional Analysis and Related Fields, edited by F. Browder, Springer-Verlag, Berlin, 1970.
[6] De Giorgi, E., Una estensione del teorema di, Bernstein,Ann. Scuola Norm. Sup. Pisa, III, 19, (1965), 79–85.
[7] Fleming, W. H., On the oriented Plateau problem, Rend. Circ. Mat., Palermo, 2 (1962), 1–22. · Zbl 0107.31304
[8] Heinz, E., Über die Lösungen der Minimalflächengleichung,Nachr. Akad. Wiss. Göttingen Math., Phys. K1 II, (1952), 51–56. · Zbl 0048.15401
[9] Hoffman, D. & Spruck, J, Sobolev inequalities on Riemannian manifolds. To appear inComm. Pure Appl. Math.
[10] Morrey, C. B.,Multiple integrals in the calculus of variations. New York, Springer-Verlag, 1966. · Zbl 0142.38701
[11] Osserman, R.,A survey of minimal surfaces. Van Nostrand Reinhold Math. Studies, 1969. · Zbl 0209.52901
[12] Simons, J., Minimal varieties in Reimannian manifolds,Ann. of Math., 88 (1968), 62–105. · Zbl 0181.49702 · doi:10.2307/1970556
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.