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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 216, Pages 57–65
DOI: https://doi.org/10.36535/0233-6723-2022-216-57-65 (Mi into1081) 		 
Some problems of convex analysis in the Lobachevsky space

A. V. Kostin, N. N. Kostina

Elabuga Branch of Kazan (Volga Region) Federal University
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DOI: https://doi.org/10.36535/0233-6723-2022-216-57-65
Abstract: 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, horocycle.
Document Type: Article
UDC: 514.13; 514.752
MSC: 53A35, 53B30
Language: Russian
Citation: A. V. Kostin, N. N. Kostina, “Some problems of convex analysis in the Lobachevsky space”, Algebra, geometry, differential equations, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 216, VINITI, Moscow, 2022, 57–65
Citation in format AMSBIB
\Bibitem{KosKos22}
\by A.~V.~Kostin, N.~N.~Kostina
\paper Some problems of convex analysis in the Lobachevsky space
\inbook Algebra, geometry, differential equations
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 216
\pages 57--65
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1081}
\crossref{https://doi.org/10.36535/0233-6723-2022-216-57-65}
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