The Bernstein Theorem in Higher Dimensions
Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 2, pp. 349-359.

Voir la notice de l'article provenant de la source 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.
@article{BUMI_2008_9_1_2_a3,
     author = {Massari, Umberto and Miranda, Mario and Miranda, Michele Jr.},
     title = {The {Bernstein} {Theorem} in {Higher} {Dimensions}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {349--359},
     publisher = {mathdoc},
     volume = {Ser. 9, 1},
     number = {2},
     year = {2008},
     zbl = {1217.49032},
     mrnumber = {2424298},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_2_a3/}
}
TY  - JOUR
AU  - Massari, Umberto
AU  - Miranda, Mario
AU  - Miranda, Michele Jr.
TI  - The Bernstein Theorem in Higher Dimensions
JO  - Bollettino della Unione matematica italiana
PY  - 2008
SP  - 349
EP  - 359
VL  - 1
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_2_a3/
LA  - en
ID  - BUMI_2008_9_1_2_a3
ER  - 
%0 Journal Article
%A Massari, Umberto
%A Miranda, Mario
%A Miranda, Michele Jr.
%T The Bernstein Theorem in Higher Dimensions
%J Bollettino della Unione matematica italiana
%D 2008
%P 349-359
%V 1
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_2_a3/
%G en
%F BUMI_2008_9_1_2_a3
Massari, Umberto; Miranda, Mario; Miranda, Michele Jr. The Bernstein Theorem in Higher Dimensions. Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 2, pp. 349-359. http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_2_a3/

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

[2] D. Benarros, I coni di Lawson e il Teorema di Bernstein PhD Thesis, University of Trento, unpublished, 1994.

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

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

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

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

[7] E. De Giorgi, 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, Pisa 1961. | MR

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

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

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

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

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

[13] M. Miranda, 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. | fulltext EuDML | MR | Zbl

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

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

[16] Mario Miranda, A nontrivial solution to the minimal surface equation in $\mathbb{R}^8$. 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 | Zbl

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

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

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