Geodesic
Some problems of convex analysis in the Lobachevsky space
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 216 (2022), pp. 57-65

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The shadow problem in the Euclidean space was posed by G. Khudaiberganov in 1982. Its solution for dimensions ${>}2$ and various generalizations were obtained by a group of Ukrainian mathematicians led by Yu. B. Zelinsky in 2015. In this paper, we consider some variations of such problems and their generalizations in the Lobachevsky space and a closed lighting problem for the Lobachevsky space. In the Euclidean space, this problem was posed by V. G. Boltyansky.
Keywords: Lobachevsky space, generalized convexity, shadow problem, lighting problem, sphere, ball
Mots-clés : horocycle. 
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A. V. Kostin; N. N. Kostina. Some problems of convex analysis in the Lobachevsky space. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 216 (2022), pp. 57-65. http://geodesic.mathdoc.fr/item/INTO_2022_216_a5/