Journal of Mathematical Sciences

, Volume 211, Issue 5, pp 710–717 | Cite as

Generalized Convex Envelopes of Sets and the Problem of Shadow

  • Yurii B. Zelinskii


The principal goal of the present work is to solve the problem of shadow for any convex set with nonempty interior in the n-dimensional Euclidean space and under the action of a group of transformations. This problem can be considered as the determination of conditions ensuring the membership of a point to a generalized convex envelope of the family of sets obtained from the initial set by the action of the group of transformations.


Euclidean space sphere ball convexity linear convexity 


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institute of Mathematics of the NAS of UkraineKievUkraine

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