The Bernstein Theorem in Higher Dimensions

Umberto Massari; Mario Miranda; Michele Jr. Miranda

Bollettino dell'Unione Matematica Italiana (2008)

  • Volume: 1, Issue: 2, page 349-359
  • ISSN: 0392-4041

Abstract

top
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.

How to cite

top

Massari, Umberto, Miranda, Mario, and Miranda, Michele Jr.. "The Bernstein Theorem in Higher Dimensions." Bollettino dell'Unione Matematica Italiana 1.2 (2008): 349-359. <http://eudml.org/doc/290472>.

@article{Massari2008,
abstract = {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.},
author = {Massari, Umberto, Miranda, Mario, Miranda, Michele Jr.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {349-359},
publisher = {Unione Matematica Italiana},
title = {The Bernstein Theorem in Higher Dimensions},
url = {http://eudml.org/doc/290472},
volume = {1},
year = {2008},
}

TY - JOUR
AU - Massari, Umberto
AU - Miranda, Mario
AU - Miranda, Michele Jr.
TI - The Bernstein Theorem in Higher Dimensions
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/6//
PB - Unione Matematica Italiana
VL - 1
IS - 2
SP - 349
EP - 359
AB - 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.
LA - eng
UR - http://eudml.org/doc/290472
ER -

References

top
  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. Zbl0146.11905MR200816DOI10.2307/1970520
  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 BENARROS, D., I coni di Lawson e il Teorema di Bernstein PhD Thesis, University of Trento, unpublished, 1994. 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. Zbl0860.53003MR1356726
  4. BOMBIERI, E. - DE GIORGI, E. - GIUSTI, E., Minimal cones and the Bernstein problem. Invent. Math., 7 (1969), 243-268. Zbl0183.25901MR250205DOI10.1007/BF01404309
  5. F. E. BROWDER, editor. Mathematical developments arising from Hilbert problems. American Mathematical Society, Providence, R. I., 1976. MR419125
  6. DE GIORGI, E., Frontiere orientate di misura minima. Seminario di Matematica della Scuola Normale Superiore di Pisa, Editrice Tecnico Scientifica, Pisa, 1961. Zbl0296.49031MR179651
  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. MR179650
  8. DE GIORGI, E. - COLOMBINI, F. - PICCININI, L. C., Frontiere orientate di misura minima e questioni collegate. Scuola Normale Superiore, Pisa, 1972. Zbl0296.49031MR493669
  9. DE GIORGI, E., Una estensione del teorema di Bernstein. Ann. Scuola Norm. Sup. Pisa (3), 19 (1965), 79-85. MR178385
  10. DE GIORGI, E., Selected papers. Springer-Verlag, Berlin, 2006. MR2229237DOI10.1007/978-3-642-41496-1
  11. FLEMING, W. H., On the oriented Plateau problem. Rend. Circ. Mat. Palermo (2), 11 (1962), 69-90. Zbl0107.31304MR157263DOI10.1007/BF02849427
  12. MASSARI, U. - MIRANDA, M., A remark on minimal cones. Boll. Un. Mat. Ital. A (6), 2 (1) (1983), 123-125. Zbl0518.49030MR694754
  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. Zbl0137.08201MR181918
  14. MIRANDA, M., Grafici minimi completi, Ann. Univ. Ferrara, 23 (1977), 269-272. MR467551
  15. MIRANDA, M., Superfici minime illimitate, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 4, n. 2 (1977), 313-322. MR500423
  16. MIRANDA, MARIO, A nontrivial solution to the minimal surface equation in 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. Zbl0792.49028MR1260469
  17. NITSCHE, J. C. C., Elementary proof of Bernstein's theorem on minimal surfaces. Ann. of Math. (2), 66 (1957), 543-544. Zbl0079.37702MR90833DOI10.2307/1969907
  18. SIMONS, J.. Minimal varieties in riemannian manifolds. Ann. of Math. (2), 88 (1968), 62-105. Zbl0181.49702MR233295DOI10.2307/1970556
  19. WOLFRAM, S., The Mathematica® book. Fourth edition. Wolfram Media, Inc., Champaign, IL, Cambridge University Press, Cambridge, 1999. MR1721106

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.