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On the unique determination of compact convex sets from their projections. The complex case

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References

  1. V. P. Golubyatnikov, “On unique reconstructibility of convex and visible compact sets from their projections. I, II,” Mat. Sb.,182, No. 5, 611–621 (1991); Sibirsk. Mat. Zh.,36, No. 2, 301–307 (1995).

    Google Scholar 

  2. V. P. Golubyatnikov, “On the unique determination of visible bodies by their projections,” Sibirsk. Mat. Zh.,29, No. 3, 92–96 (1988).

    MATH  MathSciNet  Google Scholar 

  3. L. A. Zîzenberg and A. P. Yuzhakov, Integral Representations and Residues in Multidimensional Complex Analysis [in Russian], Nauka, Novosibirsk (1979).

    Google Scholar 

  4. A. D. Alexandrov, “To the theory of mixed volumes of convex bodies,” Mat. Sb.,2, No. 6, 1205–1234 (1937).

    Google Scholar 

  5. R. J. Gardner, Geometric Tomography, Cambridge Univ. Press, Cambridge (1995).

    MATH  Google Scholar 

  6. J. F. Adams, “Vector fields on spheres,” Ann. Math.,75, No. 3, 603–632 (1962).

    Article  Google Scholar 

  7. C. M. Petty and J. R. McKinney, “Convex bodies with circumscribing boxes of constant volume,” Portugal. Math.,44, No. 4, 447–453 (1987).

    MATH  MathSciNet  Google Scholar 

  8. R. J. Gardner and A. Volĉiĉ, “Convex bodies with similar projections,” Proc. Amer. Math. Soc.,121, 563–568 (1994).

    Article  MATH  MathSciNet  Google Scholar 

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Additional information

To Yuriî Grigor'evich Reshetnyak on his 70th anniversary with great respect.

The research was supported by a grant of the Ministry of Education of the Russian Federation for Fundamental Sciences.

Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 40, No. 4, pp. 805–810, July–August, 1999.

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Golubyatnikov, V.P. On the unique determination of compact convex sets from their projections. The complex case. Sib Math J 40, 678–681 (1999). https://doi.org/10.1007/BF02675668

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