Tomter, Per The spherical Bernstein problem in even dimensions and related problems. (English) Zbl 0631.53047 Acta Math. 158, 189-212 (1987). This article contains the details of the one published in Bull. Am. Math. Soc. 11, 183-185 (1984; Zbl 0556.53037). Reviewer: D.Ferus Cited in 5 Documents MSC: 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) Keywords:Bernstein theorem; minimal spheres; isoparametric families Citations:Zbl 0556.53037 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Almgren Jr., F. J., Some interior regularity theorems for minimal surfaces and an extension of Bernstein’s theorem.Ann. of Math. (2), 84 (1966), 277–292. · Zbl 0146.11905 · doi:10.2307/1970520 [2] Bernstein, S. N., Sur un théoreme de géométrie et ses applications aux équations aux dérivées partielles du type elliptique.Comm. Inst. Sci. Math. Mech. Univ. Kharkov, 15 (1915), 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] Brieskorn, E., Beispiele zur Differentialtopologie von Singularitäten.Invent. Math., 2 (1966), 1–14. · Zbl 0145.17804 · doi:10.1007/BF01403388 [5] Calabi, E., Minimal immersions of surfaces in Euclidean spheres.J. Differential Geom., 1 (1967), 111–125. · Zbl 0171.20504 [6] do Carmo, M. P.,Differential geometry of curves and surfaces. Prentice-Hall, Inc. 1976. · Zbl 0326.53001 [7] Chern, S. S., Differential geometry, its past and future.Actes, Congr. Intern. Math., Tome 1 (1970), 41–53. [8] De Giorgi, E., Una extensione del theorema di Bernstein.Ann. Scuola Norm. Sup Pisa, 19 (1965), 79–80. [9] Hsiang, W. Y., Minimal cones and the spherical Bernstein problem I.Ann. of Math., 118 (1983), 61–73. · Zbl 0522.53051 · doi:10.2307/2006954 [10] –, Minimal cones and the spherical Bernstein problem II.Invent. Math., 74 (1983), 351–369. · Zbl 0532.53045 · doi:10.1007/BF01394241 [11] Hsiang, W. T. &Hsiang, W. Y., On the existence of codimension one minimal spheres in compact symmetric spaces of rank 2, II.J. Differential Geom., 17 (1982), 582–594. · Zbl 0503.53044 [12] Hsiang, W. T. &Lawson, Jr., H. B., Minimal submanifolds of low cohomogeneity.J. Differential Geom., 5 (1970), 1–37. · Zbl 0219.53045 [13] Hsiang, W. T., Hsiang, W. Y. &Tomter, P., On the construction of infinitely many mutually noncongruent examples of minimal imbeddings ofS 2n intoCP n ,n.Bull. Amer. Math. Soc., 8 (1983), 463–465. · Zbl 0509.53047 · doi:10.1090/S0273-0979-1983-15122-4 [14] Lawson, H. B., The equivariant Plateau problem and interior regularity.Trans. Amer. Math. Soc., 173 (1972), 231–250. · Zbl 0279.49043 · doi:10.1090/S0002-9947-1972-0308905-4 [15] O’Neill, B., The fundamental equations of a submersion.Michigan Math. J., 13 (1966), 459–469. · Zbl 0145.18602 · doi:10.1307/mmj/1028999604 [16] Simons, J., Minimal varieties in riemannian manifolds.Ann. of Math. (2), 88 (1968), 62–105. · Zbl 0181.49702 · doi:10.2307/1970556 [17] Tomter, P., The spherical Bernstein problem in even dimensions.Bull. Amer. Math. Soc. To appear. · Zbl 0556.53037 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.