Some generalisation of the shadow problem in the Lobachevsky space
UDC 514.13, 515.12, 513.83, 517.5 We consider the problem of shadow in the Lobachevsky space. This problem can be treated as the problem of finding the conditions that ensure that the points belong to the generalized convex hull of a family of sets. We determine the boundary values of parameters, fo...
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| Date: | 2021 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2397 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 514.13, 515.12, 513.83, 517.5
We consider the problem of shadow in the Lobachevsky space. This problem can be treated as the problem of finding the conditions that ensure that the points belong to the generalized convex hull of a family of sets. We determine the boundary values of parameters, for which the same configurations of balls ensure that the point belongs to a generalized convex hull of balls in the Euclidean and hyperbolic spaces. In addition to balls, we consider families of horoballs, as well as combinations of balls and horoballs. |
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| DOI: | 10.37863/umzh.v73i1.2397 |