The boundary value Minkowski problem. The parametric case

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1. [1] A.D. Aleksandrov, Convex Polyhedrons, GITTL, M.-L., 1950. 
2. [2] H. Busemann, Convex Surfaces, Interscience, New York, 1958. Zbl0196.55101MR105155
3. [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. Zbl0113.30104MR106487
4. [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. Zbl0363.53030MR423267
5. [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. Zbl0347.35019
6. [6] H. Gluck, The generalized Minkowski problem in differential geometry in the large, Ann. of Math., 96 (1972), no. 2, pp. 245-276. Zbl0243.53046MR309021
7. [7] H. Lewy, On differential geometry in the large, I (Minkowski problem), Trans. Amer. Math. Soc., 43 (1938), pp. 258-270. Zbl0018.17403MR1501942JFM64.0714.03
8. [8] C. Miranda, Partial Differential Equations of Elliptic Type, Second Edition, Ergebnisse der Mathematik, Band 2, Springer, New York, 1970. Zbl0198.14101MR284700
9. [9] L. Nirenberg, The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math., 6 (1953), pp. 337-394. Zbl0051.12402MR58265
10. [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. Zbl0511.53065MR704034
11. [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. Zbl0399.53016MR523622
12. [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). Zbl0048.40501MR52807
13. [13] A.V. Pogorelov, Extrinsic Geometry of Convex Surfaces, Translations of mathematical monographs, V. 35, Amer. Math. Soc., 1973. Zbl0311.53067MR346714
14. [14] A.V. Pogorelov, Multidimensional Minkowski Problem, Engl. transl.: John Wiley and Sons, New York, 1978. MR478079
15. [15] A.V. Pogorelov, An analogue of Minkowski problem for complete infinite convex hypersurfaces, DAN USSR (1980), pp. 553-556. Zbl0448.53042MR557787