TY - JOUR
AU - A. V. Kostin
PY - 2021/01/22
Y2 - 2022/08/16
TI - Some generalisation of the shadow problem in the Lobachevsky space
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 73
IS - 1
SE - Research articles
DO - 10.37863/umzh.v73i1.2397
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/2397
AB - UDC 514.13, 515.12, 513.83, 517.5We 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.
ER -