Problem of Shadow in the Lobachevskii Space
- 29 Downloads
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.
Unable to display preview. Download preview PDF.
- 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).Google Scholar
- 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).Google Scholar
- 5.Y. B. Zelinskii, “Problem of shadow (complex case),” Adv. Math.: Sci. J., 5, No. 1, 1–5 (2016).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.Google Scholar
- 8.G. Khudaiberganov, On a Homogeneous Polynomially Convex Hull of the Union of Balls [in Russian], VINITI, 21, 1772–1785 (1982).Google Scholar
- 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
- 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