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On the Gauss curvature of minimal surfaces


Author: Robert Osserman
Journal: Trans. Amer. Math. Soc. 96 (1960), 115-128
MSC: Primary 53.00
DOI: https://doi.org/10.1090/S0002-9947-1960-0121723-7
MathSciNet review: 0121723
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  • [1] L. Bers, Isolated singularities of minimal surfaces, Ann. of Math. vol. 53 (1951) pp. 364-386. MR 0043335 (13:244c)
  • [2] C. Blanc and F. Fiala, Le type d'une surface et sa courbure totale, Comment. Math. Helv. vol. 14 (1941-1942) pp. 230-233. MR 0006857 (4:53d)
  • [3] E. Heinz, Über die Lösungen der Minimalflächengleichung, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. (1952) pp. 51-56. MR 0054182 (14:885c)
  • [4] E. Hopf, On an inequality for minimal surfaces $ z = z(x,y)$, J. Rat. Mech. Anal. vol. 2 (1953) pp. 519-522. MR 0055735 (14:1119d)
  • [5] J. Nitsche, Über eine mit der Minimalflächengleichung zusammenhängender analytische Funktion und der Bernstein'schen Satz, Arch. Math. vol. 7 (1956) pp. 417-419. MR 0087983 (19:448c)
  • [6] -, On harmonic mappings, Proc. Amer. Math. Soc. vol. 9 (1958) pp. 268-271. MR 0104233 (21:2990a)
  • [7] -, On an estimate for the curvature of minimal surfaces $ z = z(x,y)$, J. Math. Mech. vol. 7 (1958) pp. 767-770. MR 0104234 (21:2990b)
  • [8] R. Osserman, Remarks on minimal surfaces, Comm. Pure Appl. Math. vol. 12 (1959) pp. 233-239. MR 0107868 (21:6590)
  • [9] -, Proof of a conjecture of Nirenberg, Comm. Pure Appl. Math. vol. 12 (1959) pp. 229-232. MR 0105700 (21:4436)
  • [10] -, An analogue of the Heinz-Hopf inequality, J. Math. Mech. vol. 8 (1959) pp. 383-385. MR 0104236 (21:2991)
  • [11] -, An extension of certain results in function theory to a class of surfaces, Proc. Nat. Acad. Sci. U.S.A. vol. 45 (1959) pp. 1031-1035. MR 0109323 (22:209)
  • [12] T. Radó, The problem of Plateau, Ergebn. d. Math. vol. 2(2), Berlin, 1933.

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DOI: https://doi.org/10.1090/S0002-9947-1960-0121723-7
Article copyright: © Copyright 1960 American Mathematical Society

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