Geodesic
The uniqueness of the solution in Christoffel and Minkowski problems for open surfaces
Matematičeskie zametki, Tome 13 (1973) no. 1, pp. 41-49

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We prove uniqueness in the Minkowski problem for open surfaces with spherical image greater than a hemisphere. We extend the class of regions determined earlier by Volkov and the author in which the Christoffel problem has a unique solution. 
@article{MZM_1973_13_1_a4,
     author = {V. I. Oliker},
     title = {The uniqueness of the solution in {Christoffel} and {Minkowski} problems for open surfaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {41--49},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_1_a4/}
}
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V. I. Oliker. The uniqueness of the solution in Christoffel and Minkowski problems for open surfaces. Matematičeskie zametki, Tome 13 (1973) no. 1, pp. 41-49. http://geodesic.mathdoc.fr/item/MZM_1973_13_1_a4/