Geodesic
Unique determination of three-dimensional convex polyhedral domains by relative conformal moduli of boundary condensers
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 4, pp. 3-17

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We continue the study of the problem on unique determination of domains in Euclidean spaces by the relative conformal moduli of their boundary condensers. The main result asserts that every convex bounded polyhedral domain in the three-dimensional Euclidean space is uniquely determined by the relative conformal moduli of its boundary condensers. An analogous result was earlier obtained for $n$-dimensional polyhedral domains in the case $n \ge 4$.
Keywords: $p$-modulus of a path family, boundary condenser, conformal mapping, isometry
Mots-clés : unique determination. 
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     author = {V. V. Aseev and A. P. Kopylov},
     title = {Unique determination of three-dimensional convex polyhedral domains by relative conformal moduli of boundary condensers},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {3--17},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2017_17_4_a0/}
}
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V. V. Aseev; A. P. Kopylov. Unique determination of three-dimensional convex polyhedral domains by relative conformal moduli of boundary condensers. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 4, pp. 3-17. http://geodesic.mathdoc.fr/item/VNGU_2017_17_4_a0/