Literature Cited
A. D. Aleksandrov, Intrinsic Geometry of Convex Surfaces [in Russian], Gostekhizdat, Moscow-Leningrad (1948).
M. Berge, Geometry [Russian translation], Vol. 1, Mir, Moscow (1984).
V. A. Aleksandrov and A. P. Kopylov, “Boundary values of quasi-isometric maps and unique determination of closed convex surfaces,” Symposium on Geometry in the Large and the Foundations of Relativity Theory. Novosibirsk, September 1982. Abstracts of Lectures [in Russian], Inst. Mat. Sibirsk. Otd. Akad. Nauk SSSR, Novosibirsk (1982), pp. 3–4.
V. A. Aleksandrov, “Isometry of domains in Rn and relative isometry of their boundaries. I,” Sib. Mat. Zh.,25, No. 3, 3–13 (1984).
V. A. Aleksandrov, “Isometry of domains in Rn and relative isometry of their boundaries. II,” Sib. Mat. Zh.,26, No. 6, 3–8 (1985).
V. A. Aleksandrov, “On domains which are uniquely determined by the relative metrics of their boundaries,” Trudy Inst. Mat. Akad. Nauk SSSR, Sibirsk. Otd.,7: Research in Geometry and Mathematical Analysis [in Russian] (1987), pp. 5–19.
V. A. Aleksandrov, “Unique determination of domains with non-Jordan boundaries,” 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. 3.
Ibid., Sib. Mat. Zh.,30, No. 1, 3–12 (1989).
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.
Yu. A. Volkov, “Estimate of the deformation of a convex surface depending on the change in its intrinsic metric,” Ukr. Geometr. Sb., Khar'kov, Nos. 5/6, 44–69 (1968).
A. P. Kopylov, “On boundary values of maps which are nearly isometric,” Sib. Mat. Zh.,25, No. 3, 120–131 (1984).
W. Blaschke, Kreis und Kugel [Russian translation], Nauka, Moscow (1967).
Additional information
Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 5, pp. 3–9, September–October, 1990.
Rights and permissions
About this article
Cite this article
Aleksandrov, V.A. Estimate of the deformation of a strictly convex domain as a function of the change in the relative metric of its boundary. Sib Math J 31, 711–716 (1990). https://doi.org/10.1007/BF00974483
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00974483