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Bernstein's problem

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In differential geometry, Bernstein's problem is the problem of whether entire solutions of the minimal surface equation in n-dimensional Euclidean space are linear.

References

  • Almgren, F. J. (1966), "Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem", Annals of Mathematics. Second Series, 84: 277–292, ISSN 0003-486X, MR0200816
  • Bombieri, Enrico; De Giorgi, Ennio; Giusti, E. (1969), "Minimal cones and the Bernstein problem", Inventiones Mathematicae, 7: 243–268, doi:10.1007/BF01404309, ISSN 0020-9910, MR0250205
  • De Giorgi, Ennio (1965), "Una estensione del teorema di Bernstein", Ann. Scuola Norm. Sup. Pisa (3), 19: 79–85, MR0178385
  • Fleming, Wendell H. (1962), "On the oriented Plateau problem", Rendiconti del Circolo Matematico di Palermo. Serie II, 11: 69–90, doi:10.1007/BF02849427, ISSN 0009-725X, MR0157263
  • Sabitov, I.Kh. (2001) [1994], "Bernstein theorem", Encyclopedia of Mathematics, EMS Press
  • Simons, James (1968), "Minimal varieties in riemannian manifolds", Annals of Mathematics. Second Series, 88: 62–105, ISSN 0003-486X, MR0233295
  • Straume, E. (2001) [1994], "Bernstein problem in differential geometry", Encyclopedia of Mathematics, EMS Press
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