The Bernstein-Osserman-Xavier theorems
Théorie des variétés minimales et applications, Astérisque no. 154-155  (1987), p. 95-113
@incollection{AST_1987__154-155__95_0,
     author = {O'Shea, Donal B.},
     title = {The Bernstein-Osserman-Xavier theorems},
     booktitle = {Th\'eorie des vari\'et\'es minimales et applications},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {154-155},
     year = {1987},
     pages = {95-113},
     zbl = {0635.53036},
     mrnumber = {955061},
     language = {en},
     url = {http://www.numdam.org/item/AST_1987__154-155__95_0}
}
O'Shea, Donal B. The Bernstein-Osserman-Xavier theorems, in Théorie des variétés minimales et applications, Astérisque, no. 154-155 (1987), pp. 95-113. http://www.numdam.org/item/AST_1987__154-155__95_0/

[1] L. V. Ahlfors and L. Sario, Riemann surfaces, Princeton University Press, Princeton, New Jersey, 1960. | Article | MR 114911

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

[3] S. Bernstein, Sur un théorème de géométrie et ses applications aux équations aux dérivées partielles du type elliptique, Comm. de la Soc. Math. de Kharkov (2ème série) 15 (1915-17), 38-45. | JFM 48.0811.01

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

[5] S. S. Chern, An elementary proof of the existence of isothermal parameters on a surface, Proc. Amer. Math. Soc. 6 (1955), 771-782. | Article | MR 74856 | Zbl 0066.15402

[6] S. S. Chern, Minimal surfaces in a Euclidean space of N dimensions, in Differential and Combinatorial Topology, Symposium in honor of Marston Morse, Princeton University Press, Princeton, 1965, 187-198. | MR 180926 | Zbl 0136.16701

[7] S. S. Chern and R. Osserman, Complete minimal surfaces in Euclidean n-space, J. Anal. Math. 19 (1967), 15-34. | Article | MR 226514 | Zbl 0172.22802

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

[9] W. H. Fleming, On the oriented Plateau problem, Rend. Circ. Mat. Palermo 2 (1962), 1-22. | MR 157263 | Zbl 0107.31304

[10] W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, 1964. | MR 164038 | Zbl 0115.06203

[11] D. A. Hoffman and R. Osserman, The geometry of the generalized Gauss map, Memoirs of the Amer. Math. Soc. 28, 236 (1980). | Article | MR 587748 | Zbl 0469.53004

[12] H. B. Lawson Jr., Lectures on minimal submanifolds, vol. 1, Publish or Perish Inc., Berkeley, 1980 (reprinted from IMPA (1973)). | MR 576752 | Zbl 0434.53006

[13] H. B. Lawson, this volume.

[14] R. Osserman, Proof of a conjecture of Nirenberg, Comm. Pure Appl. Math. 12 (1959), 229-232. | Article | MR 105700 | Zbl 0086.36202

[15] R. Osserman, Minimal surfaces in the large, Comment. Math. Helv. 35 (1961), 65-76. | Article | MR 123248 | Zbl 0098.34904

[16] R. Osserman, Global properties of minimal surfaces in E 3 and E n , Ann. Math. 2, 80 (1964), 340-364. | Article | MR 179701 | Zbl 0134.38502

[17] R. Osserman, A survey of minimal surfaces, Van Nostrand, New York, 1969. | MR 256278 | Zbl 0209.52901

[18] R. Schoen, L. Simon and S. T. Yau, Curvature estimates for minimal hypersurfaces, Acta Math. 134 (1975), 275-288. | Article | MR 423263 | Zbl 0323.53039

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

[20] K. Voss, Über vollständige Minimalflächen, L'Enseignement Math. 10 (1964), 316-317.

[21] F. Xavier, The Gauss map of a complete non-flat minimal surface cannot omit 7 points of the sphere, Ann. Math. 113 (1981), 211-214. | Article | MR 604048 | Zbl 0477.53007

[22] F. Xavier, Erratum to the Daper "The Gauss map of a complete non-flat minimal surface cannot omit 7 points of the sphere", Ann. Math. 115 (1982), 667. | Article | MR 657243 | Zbl 0485.53006

[23] S. T. Yau, Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana U. Math. J. 25 (1976), 659-670. | Article | MR 417452 | Zbl 0335.53041