The boundary value Minkowski problem. The parametric case
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 9 (1982) no. 3, pp. 463-490.
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     author = {Oliker, V. I.},
     title = {The boundary value {Minkowski} problem. {The} parametric case},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {463--490},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 9},
     number = {3},
     year = {1982},
     mrnumber = {681936},
     zbl = {0507.53040},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1982_4_9_3_463_0/}
}
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Oliker, V. I. The boundary value Minkowski problem. The parametric case. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 9 (1982) no. 3, pp. 463-490. http://www.numdam.org/item/ASNSP_1982_4_9_3_463_0/

[1] A.D. Aleksandrov, Convex Polyhedrons, GITTL, M.-L., 1950.

[2] H. Busemann, Convex Surfaces, Interscience, New York, 1958. | MR | Zbl

[3] E. Calabi, Improper affine hyperspheres of convex type and a generalization. of a theorem by K. Jörgens, Michigan Math. J., 5 (1958), pp. 105-126. | MR | Zbl

[4] S.Y. Cheng - S.T. Yau, On the regularity of the solution of the n-dimensional Minkowski problem, Comm. Pure Appl. Math., 29 (1976), pp. 499-516. | MR | Zbl

[5] S.Y. Cheng - S.T. Yau, On the regularity of the Monge-Ampére equation det (∂2u/∂xi ∂xj) = F(x, u), Comm. Pure Appl. Math., 30 (1977), pp. 41-68. | Zbl

[6] H. Gluck, The generalized Minkowski problem in differential geometry in the large, Ann. of Math., 96 (1972), no. 2, pp. 245-276. | MR | Zbl

[7] H. Lewy, On differential geometry in the large, I (Minkowski problem), Trans. Amer. Math. Soc., 43 (1938), pp. 258-270. | JFM | MR | Zbl

[8] C. Miranda, Partial Differential Equations of Elliptic Type, Second Edition, Ergebnisse der Mathematik, Band 2, Springer, New York, 1970. | MR | Zbl

[9] L. Nirenberg, The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math., 6 (1953), pp. 337-394. | MR | Zbl

[10] V.I. Oliker, On the linearized Monge-Ampére equations related to the boundary value Minkowski problem and its generalizations, preprint, Conference on Monge-Ampére Equations, Florence, 1980. | MR | Zbl

[11] V.I. Oliker, On certain elliptic differential equations on a hypersphere and their geometric applications, Indiana Univ. Math. J., 28 (1979), pp. 35-51. | MR | Zbl

[12] A.V. Pogorelov, Regularity of a convex surface with given Gaussian curvature, Mat. Sb., 31 (73) (1952), pp. 88-103 (see also [13], chapter 7, § 3). | MR | Zbl

[13] A.V. Pogorelov, Extrinsic Geometry of Convex Surfaces, Translations of mathematical monographs, V. 35, Amer. Math. Soc., 1973. | MR | Zbl

[14] A.V. Pogorelov, Multidimensional Minkowski Problem, Engl. transl.: John Wiley and Sons, New York, 1978. | MR

[15] A.V. Pogorelov, An analogue of Minkowski problem for complete infinite convex hypersurfaces, DAN USSR (1980), pp. 553-556. | MR | Zbl