The Bernstein Theorem in Higher Dimensions
Massari, Umberto ; Miranda, Mario ; Miranda, Michele Jr.
Bollettino dell'Unione Matematica Italiana, Tome 1 (2008), p. 349-359 / Harvested from Biblioteca Digitale Italiana di Matematica

In this work we have reconsidered the famous paper of Bombieri, De Giorgi and Giusti [4] and, thanks to the software Mathematica® we made it possible for anybody to control the difficult computations.

Publié le : 2008-06-01
@article{BUMI_2008_9_1_2_349_0,
     author = {Umberto Massari and Mario Miranda and Michele Jr. Miranda},
     title = {The Bernstein Theorem in Higher Dimensions},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {1},
     year = {2008},
     pages = {349-359},
     zbl = {1217.49032},
     mrnumber = {2424298},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2008_9_1_2_349_0}
}
Massari, Umberto; Miranda, Mario; Miranda, Michele Jr. The Bernstein Theorem in Higher Dimensions. Bollettino dell'Unione Matematica Italiana, Tome 1 (2008) pp. 349-359. http://gdmltest.u-ga.fr/item/BUMI_2008_9_1_2_349_0/

[1] Almgren, F. J., Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem. Ann. of Math. (2), 84 (1966), 277-292. | MR 200816 | Zbl 0146.11905

[2] Benarros, D., I coni di Lawson e il Teorema di Bernstein PhD Thesis, University of Trento, unpublished, 1994.

[3] Benarros, D. - Miranda, M., Lawson cones and the Bernstein theorem. Advances in geometric analysis and continuum mechanics (1995), 44-56. | MR 1356726 | Zbl 0860.53003

[4] Bombieri, E. - De Giorgi, E. - Giusti, E., Minimal cones and the Bernstein problem. Invent. Math., 7 (1969), 243-268. | MR 250205 | Zbl 0183.25901

[5] F. E. Browder, editor. Mathematical developments arising from Hilbert problems. American Mathematical Society, Providence, R. I., 1976. | MR 419125

[6] De Giorgi, E., Frontiere orientate di misura minima. Seminario di Matematica della Scuola Normale Superiore di Pisa, Editrice Tecnico Scientifica, Pisa, 1961. | MR 179651 | Zbl 0296.49031

[7] De Giorgi, E., Complementi alla teoria della misura (n-1)-dimensionale in uno spazio n-dimensionale. Seminario di Matematica della Scuola Normale Superiore di Pisa, Editrice Tecnico Scientifica, Pisa1961. | MR 179650

[8] De Giorgi, E. - Colombini, F. - Piccinini, L. C., Frontiere orientate di misura minima e questioni collegate. Scuola Normale Superiore, Pisa, 1972. | MR 493669 | Zbl 0296.49031

[9] De Giorgi, E., Una estensione del teorema di Bernstein. Ann. Scuola Norm. Sup. Pisa (3), 19 (1965), 79-85. | MR 178385

[10] De Giorgi, E., Selected papers. Springer-Verlag, Berlin, 2006. | MR 2229237

[11] Fleming, W. H., On the oriented Plateau problem. Rend. Circ. Mat. Palermo (2), 11 (1962), 69-90. | MR 157263 | Zbl 0107.31304

[12] Massari, U. - Miranda, M., A remark on minimal cones. Boll. Un. Mat. Ital. A (6), 2 (1) (1983), 123-125. | MR 694754 | Zbl 0518.49030

[13] Miranda, M., Un teorema di esistenza e unicità per il problema dell'area minima in n variabili. Ann. Scuola Norm. Sup. Pisa (3), 19 (1965), 233-249. | MR 181918 | Zbl 0137.08201

[14] Miranda, M., Grafici minimi completi, Ann. Univ. Ferrara, 23 (1977), 269-272. | MR 467551

[15] Miranda, M., Superfici minime illimitate, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 4, n. 2 (1977), 313-322. | MR 500423

[16] Miranda, Mario, A nontrivial solution to the minimal surface equation in 8. In Boundary value problems for partial differential equations and applications, volume 29 of RMA Res. Notes Appl. Math., pages 399-402. Masson, Paris, 1993. | MR 1260469 | Zbl 0792.49028

[17] Nitsche, J. C. C., Elementary proof of Bernstein's theorem on minimal surfaces. Ann. of Math. (2), 66 (1957), 543-544. | MR 90833 | Zbl 0079.37702

[18] Simons, J.. Minimal varieties in riemannian manifolds. Ann. of Math. (2), 88 (1968), 62-105. | MR 233295 | Zbl 0181.49702

[19] Wolfram, S., The Mathematica® book. Fourth edition. Wolfram Media, Inc., Champaign, IL, Cambridge University Press, Cambridge, 1999. | MR 1721106