Skip to main content
Log in

Estimate of the deformation of a strictly convex domain as a function of the change in the relative metric of its boundary

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. A. D. Aleksandrov, Intrinsic Geometry of Convex Surfaces [in Russian], Gostekhizdat, Moscow-Leningrad (1948).

    Google Scholar 

  2. M. Berge, Geometry [Russian translation], Vol. 1, Mir, Moscow (1984).

    Google Scholar 

  3. 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.

    Google Scholar 

  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).

    Google Scholar 

  5. V. A. Aleksandrov, “Isometry of domains in Rn and relative isometry of their boundaries. II,” Sib. Mat. Zh.,26, No. 6, 3–8 (1985).

    Google Scholar 

  6. 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.

    Google Scholar 

  7. 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.

    Google Scholar 

  8. Ibid., Sib. Mat. Zh.,30, No. 1, 3–12 (1989).

    Google Scholar 

  9. 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.

    Google Scholar 

  10. 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).

    Google Scholar 

  11. A. P. Kopylov, “On boundary values of maps which are nearly isometric,” Sib. Mat. Zh.,25, No. 3, 120–131 (1984).

    Google Scholar 

  12. W. Blaschke, Kreis und Kugel [Russian translation], Nauka, Moscow (1967).

    Google Scholar 

Download references

Authors

Additional information

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 5, pp. 3–9, September–October, 1990.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00974483

Keywords

Navigation