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Problem of Shadow in the Lobachevskii Space

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Ukrainian Mathematical Journal Aims and scope

We consider the problem of shadow in a hyperbolic space. This problem can be regarded as a problem of finding conditions guaranteeing that points belong to a generalized convex hull of the family of balls.

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References

  1. Yu. B. Zelinskii, I. Yu. Vygovskaya, and H. K. Dakhil, “Problem of shadow and related problems,” Proc. Intern. Geom. Center, 9, No. 3-4, 50–58 (2016).

    Google Scholar 

  2. Yu. B. Zelinskii, I. Yu. Vygovskaya, and M. V. Stefanchuk, “Generalized convex sets and the problem of shadow,” Ukr. Mat. Zh., 67, No. 12, 1658–1666 (2015); English translation: Ukr. Math. J., 67, No. 12, 1874–1883 (2016).

  3. Yu. B. Zelins’kyi and M. V. Stefanchuk, “Generalization of the shadow problem,” Ukr. Mat. Zh., 68, No. 6, 757–762 (2016); English translation: Ukr. Math. J., 68, No. 6, 862–867 (2016).

  4. Y. B. Zelinskii, “Generalized convex envelopes of sets and the problem of shadow,” J. Math. Sci., 211, No. 5, 710–717 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  5. Y. B. Zelinskii, “Problem of shadow (complex case),” Adv. Math.: Sci. J., 5, No. 1, 1–5 (2016).

  6. Y. B. Zelinskii, “The problem of the shadows,” Bull. Soc. Sci. Lett. Lódź, 66, 37 (2016).

    MathSciNet  MATH  Google Scholar 

  7. Yu. B. Zelinskii, “Shadow problem for a family of sets,” in: Proc. of the Institute of Mathematics, Ukrainian National Academy of Sciences, 12, No. 4 (2015), pp. 197–204.

  8. G. Khudaiberganov, On a Homogeneous Polynomially Convex Hull of the Union of Balls [in Russian], VINITI, 21, 1772–1785 (1982).

  9. T. M. Osipchuk and M. V. Tkachuk, “Problem of shadow for the domains in Euclidean spaces,” Ukr. Mat. Visn., 13, No. 4, 532–542 (2016).

    Google Scholar 

  10. A.V. Kostin and I. K. Sabitov, “Smarandache theorem in hyperbolic geometry,” J. Math. Phys., Anal., Geom., 10, No. 2, 221–232 (2014).

    MATH  Google Scholar 

  11. Zh. Kaidasov and E. V. Shikin, “On the isometric immersion of a convex Lobachevskii plane containing two horodisks in E 3 ,” Mat. Zametki, 39, No. 4, 612–617 (1986).

    MathSciNet  Google Scholar 

  12. B. A. Rozenfel’d, Non-Euclidean Spaces [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  13. N. M. Nestorovich, Geometric Structures in the Lobachevskii Plane [in Russian], Gostekhteorizdat, Moscow (1951).

    Google Scholar 

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Authors and Affiliations

  1. Kazan Federal University, Elabuga Institute, Elabuga, Russia

    A.V. Kostin

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  1. A.V. Kostin
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Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 11, pp. 1525–1532, November, 2018.

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Kostin, A. Problem of Shadow in the Lobachevskii Space. Ukr Math J 70, 1758–1766 (2019). https://doi.org/10.1007/s11253-019-01604-z

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  • DOI: https://doi.org/10.1007/s11253-019-01604-z

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