References
V. A. Aleksandrov, “Isometry of domains inR n and relative isometry of their boundaries,” Cand. Dissertation, Inst. Math., Siberian Branch, Acad. Sic. USSR, Novosibirsk (1986).
V. A. Aleksandrov, “Unique determination of domains with non-Jordan boundaries,” Sib. Mat. Zh.,30, No. 1, 3–12 (1989).
A. P. Kopylov, “On boundary values of maps which are nearly isometric,” Sib. Mat. Zh.,25, No. 3, 120–131 (1984).
V. A. Aleksandrov, “Isometry of domains inR n and relative isometry of their boundaries. I,” Sib. Mat. Zh.,25, No. 3, 3–13 (1984).
A. V. Kuz'minykh, “On isometry of domains whose boundaries are locally isometric in relative metrics,” Sib. Mat. Zh.,26, No. 3, 91–99 (1985).
V. A. Aleksandrov, “Isometry of domains inR n and relative isometry of their boundaries. II,” Sib. Mat. Zh.,26, No. 6, 3–8 (1985).
D. A. Trotsenko, “Unique determination of bounded domains by the metric of the boundary induced by the metric of the domain,” All-Union Conference on Geometry “in the Large”, Novosibirsk, Sept. 1987 Abstracts of Lectures [in Russian], Inst. Mat. Sibirsk. Otd. Akad. Nauk SSSR, Novosibirsk (1987), p. 122.
V. A. Aleksandrov, “On isometry of polyhedral domains whose boundaries are locally isometric in relative metrics,” Sib. Mat. Zh.,33, No. 2, 3–9 (1992).
Yu. D. Burago and V. A. Zalgaller, “Sufficient conditions for convexity,” Zapiski Nauchn. Semin., LOMI,45, 3–52 (1974).
A. D. Aleksandrov Intrinsic Geometry of Convex Surfaces [in Russian], Gostekhizdat, Moscow-Leningrad (1948).
Additional information
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 33, No.4, pp. 30–41, July–August, 1992.
Translated by N. S. Dairbekov
Rights and permissions
About this article
Cite this article
Borovikova, M.K. On isometry of polygonal domains with boundaries locally isometric in relative metrics. Sib Math J 33, 571–580 (1992). https://doi.org/10.1007/BF00971122
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00971122