Geodesic
Unique determination of~conformal type for~domains.~II
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1205-1214.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article is the second part of a review series entitled “Unique determination of conformal type for domains”, initiated by the author's eponymous paper, published in Sib. Èlektron. Mat. Izv., 16, 692–708 (2019). The main result of the present article is that any convex bounded polyhedral domain in the three-dimensional Euclidean space is uniquely determined by the relative conformal moduli of its boundary condensers.
Keywords: $p$-modulus of a family of paths, boundary condenser, quasiconformal mapping, conformal mapping, isometric mapping
Mots-clés : unique determination. 
@article{SEMR_2019_16_a126,
     author = {A. P. Kopylov},
     title = {Unique determination of~conformal type {for~domains.~II}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1205--1214},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a126/}
}
TY  - JOUR
AU  - A. P. Kopylov
TI  - Unique determination of~conformal type for~domains.~II
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 1205
EP  - 1214
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a126/
LA  - en
ID  - SEMR_2019_16_a126
ER  - 
%0 Journal Article
%A A. P. Kopylov
%T Unique determination of~conformal type for~domains.~II
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 1205-1214
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a126/
%G en
%F SEMR_2019_16_a126
A. P. Kopylov. Unique determination of~conformal type for~domains.~II. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1205-1214. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a126/

[1] A.P. Kopylov, “Unique determination of conformal type for domains”, Sib. Elektron. Mat. Izv., 16 (2019), 692–708 | MR | Zbl

[2] A.P. Kopylov, “Unique determination of convex polyhedral domains by relative conformal moduli of boundary condensers”, Dokl. Math., 74:2 (2006), 637–639 | DOI | MR | Zbl

[3] A.P. Kopylov, “On the unique determination of domains in Euclidean spaces”, J. of Math. Sciences, 153:6 (2008), 869–898 | DOI | MR | Zbl

[4] A.P. Kopylov, “Unique determination of domains”, Differential Geometry and its Applications, Proceedings of International Conference DGA 2007 in Honour of L. Euler (Olomouc, 2007), World Scientific, Singapore, 2008, 157–169 | DOI | MR | Zbl

[5] A.P. Kopylov, “Unique determination of convex polyhedral domains in three-dimensional Euclidean space by relative conformal moduli of boundary condensers”, Dokl. Math., 84:3 (2011), 789–790 | DOI | MR | Zbl

[6] V.V. Aseev, A.P. Kopylov, “Unique determination of three-dimensional convex polyhedral domains by relative conformal moduli of boundary condensers”, Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki, 17:4 (2017), 3–17 | MR

[7] Yu.G. Reshetnyak, Stability Theorems in Geometry and Analysis, Kluwer Academic Publishers, Dordrecht, 1994 | MR | Zbl

[8] A.D. Aleksandrov, N. Yu. Netsvetaev, Geometry, BXV-Peterburg, St. Petersburg, 2010 (in Russian) | MR

[9] A.D. Aleksandrov, Geometry, v. 2, Convex Polyhedra, Nauka, Novosibirsk, 2007 (in Russian) | MR | Zbl

[10] M.A. Lavrent'ev, B.V. Shabat, Methods for the Theory of Functions of a Complex Variable, Nauka, M., 1987 (in Russian) | Zbl

[11] J. Väisälä, Lectures on $n$-Dimensional Quasiconformal Mappings, Springer, Berlin–Heidelberg–New York, 1973 | MR

[12] F.W. Gehring, J. Väisälä, “The coefficients of quasiconformality of domains in space”, Acta Mathematica, 114:1–2 (1965), 1–70 | DOI | MR | Zbl