Geodesic
On the problem of determining the Riemannian metric $ds^2=\lambda^2(x)|dx|^2$
Matematičeskie zametki, Tome 16 (1974) no. 4, pp. 611-617 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the problem of determining the Riemannian metric, defined in a domain, if the distances in this metric between points of the boundary of the domain are known. 
@article{MZM_1974_16_4_a13,
     author = {Yu. E. Anikonov},
     title = {On the problem of determining the {Riemannian} metric $ds^2=\lambda^2(x)|dx|^2$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {611--617},
     year = {1974},
     volume = {16},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_4_a13/}
}
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Yu. E. Anikonov. On the problem of determining the Riemannian metric $ds^2=\lambda^2(x)|dx|^2$. Matematičeskie zametki, Tome 16 (1974) no. 4, pp. 611-617. http://geodesic.mathdoc.fr/item/MZM_1974_16_4_a13/