Skip to main content
Log in

Smoothness of the metric of spaces with two-sided bounded Aleksandrov curvature

  • 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. Alexandrow, “Über eine Verallgemeinerung der Riemannschen Geometrie,” Schriftenreihe Inst. Math. Dtsch. Akad. Wiss.,1, 33–84 (1957).

    Google Scholar 

  2. A. D. Aleksandrov, “A theorem on triangles in a metric space and some applications of it,” Tr. Mat. Inst. Akad. Nauk SSSR,38, 5–23 (1951).

    Google Scholar 

  3. I. G. Nikolaev, “On parallel displacement of vectors in space with two-sided bounded Aleksandrov curvature,” Sib. Mat. Zh.,24, No. 1, 130–145 (1983).

    Google Scholar 

  4. V. N. Berestovskii, “Introduction of a Riemannian structure in certain metric spaces,” Sib. Mat. Zh.,16, No. 4, 651–662 (1975).

    Google Scholar 

  5. S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics, Amer. Math. Soc. (1969).

  6. S. M. Nikol'skii, Approximation of Functions of Several Variables and Embedding Theorems [in Russian], 2nd revised ed., Nauka, Moscow (1977).

    Google Scholar 

  7. O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press (1968).

  8. I. Kh. Sabitov and S. Z. Shefel', “On connections between the orders of smoothness of a surface and its metric,” Sib. Mat. Zh.,17, 916–925 (1976).

    Google Scholar 

  9. S. K. Vodol'yanov, V. M. Gol'dshtein, and Yu. G. Reshetnyak, “On geometric properties of functions with first generalized derivatives,” Usp. Mat. Nauk,34, No. 1, 17–66 (1979).

    Google Scholar 

  10. I. G. Nikolaev, “Parallel displacement and smoothness of the metric of spaces with bounded curvature,” Dokl. Akad. Nauk SSSR,250, 1056–1058 (1980).

    Google Scholar 

  11. D. Gromoll, W. Klingenberg, and W. Meyer, Riemannsche Geometrie im Grossen, Springer-Verlag, Berlin-Heidelberg-New York (1968).

    Google Scholar 

  12. L. Bers, F. John, and M. Schechter, Partial Differential Equations, Wiley-Interscience, New York-London-Sydney (1964).

    Google Scholar 

Download references

Authors

Additional information

Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk. translated from Sibirskii Matematicheskii Zhurnal, Vol. 24, No. 2, pp. 114–132, March–April, 1983.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nikolaev, I.G. Smoothness of the metric of spaces with two-sided bounded Aleksandrov curvature. Sib Math J 24, 247–263 (1983). https://doi.org/10.1007/BF00968740

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00968740

Navigation