Geodesic
Uniqueness of the solution of Christoffel's problem for nonclosed surfaces
Matematičeskie zametki, Tome 8 (1970) no. 2, pp. 251-257.

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Conditions satisfied by a region of a sphere are found under which the differential equation arising in the solution of Christoffel's problem has not more than one solution in the region taking given boundary values. 
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     author = {Yu. A. Volkov and V. I. Oliker},
     title = {Uniqueness of the solution of {Christoffel's} problem for nonclosed surfaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {251--257},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_2_a13/}
}
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Yu. A. Volkov; V. I. Oliker. Uniqueness of the solution of Christoffel's problem for nonclosed surfaces. Matematičeskie zametki, Tome 8 (1970) no. 2, pp. 251-257. http://geodesic.mathdoc.fr/item/MZM_1970_8_2_a13/