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. 
@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/}
}
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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://archive.numdam.org/item/ASNSP_1982_4_9_3_463_0/

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