Generalized Convex Envelopes of Sets and the Problem of Shadow
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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.
KeywordsEuclidean space sphere ball convexity linear convexity
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