@article{ASNSP_1982_4_9_3_463_0, 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://archive.numdam.org/item/ASNSP_1982_4_9_3_463_0/} }
TY - JOUR AU - Oliker, V. I. TI - The boundary value Minkowski problem. The parametric case JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1982 SP - 463 EP - 490 VL - 9 IS - 3 PB - Scuola normale superiore UR - http://archive.numdam.org/item/ASNSP_1982_4_9_3_463_0/ LA - en ID - ASNSP_1982_4_9_3_463_0 ER -
%0 Journal Article %A Oliker, V. I. %T The boundary value Minkowski problem. The parametric case %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1982 %P 463-490 %V 9 %N 3 %I Scuola normale superiore %U http://archive.numdam.org/item/ASNSP_1982_4_9_3_463_0/ %G en %F ASNSP_1982_4_9_3_463_0
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://archive.numdam.org/item/ASNSP_1982_4_9_3_463_0/
[1] Convex Polyhedrons, GITTL, M.-L., 1950.
,[2] Convex Surfaces, Interscience, New York, 1958. | MR | Zbl
,[3] 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] On the regularity of the solution of the n-dimensional Minkowski problem, Comm. Pure Appl. Math., 29 (1976), pp. 499-516. | MR | Zbl
- ,[5] 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] The generalized Minkowski problem in differential geometry in the large, Ann. of Math., 96 (1972), no. 2, pp. 245-276. | MR | Zbl
,[7] On differential geometry in the large, I (Minkowski problem), Trans. Amer. Math. Soc., 43 (1938), pp. 258-270. | JFM | MR | Zbl
,[8] Partial Differential Equations of Elliptic Type, Second Edition, Ergebnisse der Mathematik, Band 2, Springer, New York, 1970. | MR | Zbl
,[9] The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math., 6 (1953), pp. 337-394. | MR | Zbl
,[10] 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] On certain elliptic differential equations on a hypersphere and their geometric applications, Indiana Univ. Math. J., 28 (1979), pp. 35-51. | MR | Zbl
,[12] 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] Extrinsic Geometry of Convex Surfaces, Translations of mathematical monographs, V. 35, Amer. Math. Soc., 1973. | MR | Zbl
,[14] Multidimensional Minkowski Problem, Engl. transl.: John Wiley and Sons, New York, 1978. | MR
,[15] An analogue of Minkowski problem for complete infinite convex hypersurfaces, DAN USSR (1980), pp. 553-556. | MR | Zbl
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