KFU. Card publication. Some generalisation of the shadow problem in the Lobachevsky space

KAZAN
FEDERAL UNIVERSITY

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SOME GENERALISATION OF THE SHADOW PROBLEM IN THE LOBACHEVSKY SPACE

Form of presentation

Articles in international journals and collections

Year of publication

2021

Язык

украинский

Authors, employees of KFU

Kostin Andrey Viktorovich, author

Bibliographic description in the original language

Kostin A. V. “Deyaki uzagalnennya zadachi pro tin v prostori Lobachevskogo”. Ukrains'kyi Matematychnyi Zhurnal, Vol. 73, no. 1, Jan. 2021, pp. 61 -68, doi:10.37863/umzh.v73i1.2397.

Annotation

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.

Keywords

problem of shadow, Lobachevsky space, generalized convexity, sphere, ball, horocycle, horosphere, horoball

The name of the journal

Ukrainian Mathematical Journal

URL

http://umj.imath.kiev.ua/index.php/umj/article/view/2397

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=246659&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Kostin Andrey Viktorovich	ru_RU
dc.date.accessioned	2021-01-01T00:00:00Z	ru_RU
dc.date.available	2021-01-01T00:00:00Z	ru_RU
dc.date.issued	2021	ru_RU
dc.identifier.citation	Kostin A. V. “Деякi узагальнення задачi про тiнь в просторi Лобачевського”. Ukrains'kyi Matematychnyi Zhurnal, Vol. 73, no. 1, Jan. 2021, pp. 61 -68, doi:10.37863/umzh.v73i1.2397.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=246659&p_lang=2	ru_RU
dc.description.abstract	Ukrainian Mathematical Journal	ru_RU
dc.description.abstract	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.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	problem of shadow	ru_RU
dc.subject	Lobachevsky space	ru_RU
dc.subject	generalized convexity	ru_RU
dc.subject	sphere	ru_RU
dc.subject	ball	ru_RU
dc.subject	horocycle	ru_RU
dc.subject	horosphere	ru_RU
dc.subject	horoball	ru_RU
dc.title	Some generalisation of the shadow problem in the Lobachevsky space	ru_RU
dc.type	Articles in international journals and collections	ru_RU