Geodesic
Uniqueness theorem for convex surfaces
Matematičeskie zametki, Tome 6 (1969) no. 1, pp. 115-117 
Yu. E. Anikonov. Uniqueness theorem for convex surfaces. Matematičeskie zametki, Tome 6 (1969) no. 1, pp. 115-117. http://geodesic.mathdoc.fr/item/MZM_1969_6_1_a13/
@article{MZM_1969_6_1_a13,
     author = {Yu. E. Anikonov},
     title = {Uniqueness theorem for convex surfaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {115--117},
     year = {1969},
     volume = {6},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_1_a13/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A proof is given of the following assertion: two closed convex analytic surfaces in three-dimensional Euclidean space are equal if their areas and lengths of boundaries of orthogonal projections onto any plane coincide.