Bernstein's problem
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
- Bernstein, S.N. (1917), "Sur une théorème de géometrie et ses applications aux équations dérivées partielles du type elliptique", Comm. Soc. Math. Kharkov, 15: 38–45
{{citation}}: Unknown parameter|month=ignored (help) - 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