Some problems of convex analysis in the Lobachevsky space

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.