Maximum principles and minimal surfaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 25 (1997) no. 3-4, p. 667-681
@article{ASNSP_1997_4_25_3-4_667_0,
     author = {Miranda, Mario},
     title = {Maximum principles and minimal surfaces},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 25},
     number = {3-4},
     year = {1997},
     pages = {667-681},
     zbl = {1015.49028},
     mrnumber = {1655536},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1997_4_25_3-4_667_0}
}
Miranda, Mario. Maximum principles and minimal surfaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 25 (1997) no. 3-4, pp. 667-681. http://www.numdam.org/item/ASNSP_1997_4_25_3-4_667_0/

[1] F.J. Almgren, JR., Some interior regularity theoremsfor minimal surfaces and an extension of Bernstein's theorem, Ann. of Math. 85 (1996), 277-292. | Zbl 0146.11905

[2] D. Benarros - M. Miranda, Lawson cones and the Bernstein theorem, Advances in Geom. Anal. and Cont. Mech., pages 44-56, 1995. Ed. P. Concus and K. Lancaster for Int. Press. | MR 1356726 | Zbl 0860.53003

[3] S. Bernstein, Sur les surfaces définies au moyen de leur courbure moyenne ou totale, Ann. Sci. Ec. Norm. Sup. 27 (1910), 233-256. | JFM 41.0692.05 | Numdam | MR 1509123

[4] L. Bers, Isolated singularities of minimal surfaces, Ann. of Math. 53 (1951), 364-386. | MR 43335 | Zbl 0043.15901

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

[6] E. Bombieri - E. De Giorgi - M. Miranda, Una maggiorazione a priori relativa alle ipersuperficie minimali non parametriche, Arch. Rat. Mech. Anal. 32 (1969), 255-267. | MR 248647 | Zbl 0184.32803

[7] E. Bombieri - E. Giusti, Harnack's inequality for elliptic differential equations on minimal surfaces, Invent. Math. 15 (1972), 24-46. | MR 308945 | Zbl 0227.35021

[8] E. De Giorgi, Su una teoria generale della misura (r - 1)-dimensionale in uno spazio euclideo ad r dimensioni, Ann. Mat. Pura Appl. 36 (1954), 191-213. | MR 62214 | Zbl 0055.28504

[9] E. De Giorgi, Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Scie. Torino Cl. Sci. Fis. Mat. Natur. 3 (1957), 25-43. | MR 93649 | Zbl 0084.31901

[10] E. De Giorgi, Una estensione del teorema di Bernstein, Ann. Sc. Norm. Sup. Pisa 19 (1965), 79-85. | Numdam | MR 178385 | Zbl 0168.09802

[11] E. De Giorgi - F. Colombini - L.C. Piccinini, "Frontiere Orientate di Misura Minima e Questioni Collegate", Pubbl. Cl. Sci. Scuola Norm. Sup. Pisa Cl. Sci., 1972. | MR 493669 | Zbl 0296.49031

[12] E. De Giorgi - G. Stampacchia, Sulle singolarità eliminabili delle ipersuperficie minimali, Rend. Acc. Lincei 38 (1965), 352-357. | MR 187158 | Zbl 0135.40003

[13] R. Finn, Isolated singularities of solutions of non-linear partial differential equations, Transact. Amer. Math. Soc. 75 (1953), 385-404. | MR 58826 | Zbl 0053.39205

[14] R. Finn, Remarks relevant to minimal surfaces and to surfaces of prescribed mean curvature, J. d'Analyse Mathém. 14 (1965), 139-160. | MR 188909 | Zbl 0163.34604

[15] W.H. Fleming, On the oriented Plateau problem, Rend. Circ. Mat. Palermo 9 (1962), 69-89. | MR 157263 | Zbl 0107.31304

[16] A. Haar, Über das Plateausche Problem, Math. Ann. 97 (1927), 124-158. | JFM 52.0710.02 | MR 1512358

[17] D. Hilbert, Über das Dirichlet'sche Prinzip, Uber. Deutsch. Math. Verein. 8 (1900), 184-188. | JFM 31.0418.01

[18] D. Hilbert, Über das Dirichlet'sche Prinzip, Math. Ann. 59 (1904), 161-186. | JFM 35.0436.02 | MR 1511266

[19] H. Jenkins - J. Serrin, The Dirichlet problem for the minimal surface equation in higher dimensions, J. Reine Angew. Math. 229 (1968), 170-187. | MR 222467 | Zbl 0159.40204

[20] H. Lebesgue, Sur le problème de Dirichlet, Rend. Circ. Mat. Palermo 24 (1907), 371-402. | JFM 38.0392.01

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

[22] M. Miranda, Un principio di massimo forte per le frontiere minimali e una sua applicazione alla soluzione del problema al contorno per l'equazione delle superfici di area minima, Rend. Sem. Mat. Padova 45 (1951), 355-366. | Numdam | MR 303390 | Zbl 0266.49034

[23] M. Miranda, Existence and regularity of hypersurfaces of Rn with prescribed mean curvature, AMS, Proc. of Symp. in Pure Math. 23 (1973), 1-9. | MR 336530 | Zbl 0274.35022

[24] M. Miranda, Grafici minimi completi, Ann. Univ. Ferrara 23 (1977), 269-272. | MR 467551 | Zbl 0367.53001

[25] M. Miranda, Sulle singolarità eliminabili delle soluzioni dell'equazione delle superfici minime, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 4 Serie IV (1977), 129-132. | Numdam | MR 433309 | Zbl 0344.35037

[26] M. Miranda, Superfici minime illimitate, Ann. Scuola Norm. Sup. Pisa Cl. Sci.4 (1977), 313-322. | Numdam | MR 500423 | Zbl 0352.49020

[27] M.P. Moschen, Principio di massimo forte per le frontiere di misura minima, Ann. Univ. Ferrara Sez. VII, Sc. Mat. 23 (1977), 165-168. | MR 482508 | Zbl 0384.49030

[28] J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577-591. | MR 159138 | Zbl 0111.09302

[29] J. Nash, Continuity of the solutions ofparabolic and elliptic equations, Amer. J. Math. 80 (1958), 931-954. | MR 100158 | Zbl 0096.06902

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

[31] J.C.C. Nitsche, On new results in the theory of minimal surfaces, Bull. Amer. Math. Soc. 71 (1965), 195-270. | MR 173993 | Zbl 0135.21701

[32] T. Rado, The problem of the least area and the problem of Plateau, Math. Z. 32 (1930), 763-796. | JFM 56.0436.01 | MR 1545197

[33] L. Simon, Entire solutions of the minimal surface equation, J. Diff. Geom. 30 (1989), 643-688. | MR 1021370 | Zbl 0687.53009

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

[35] J. Von Neumann, Über einen Hilfssatz der Variationsrechnung, Abh. Math. Sem. Hamburg Univ. 8 (1931), 28-31. | JFM 56.0440.04