Generalizations of the shadow problem

2015/11/04 by Yu. B. Zelinskii, Zelinskii, Yu. B., M. V. Stefanchuk +2
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Metric Geometry (math.MG) #math.MG

paper · pdf · doi:10.48550/arxiv.1511.01784

arxiv created 2015/11/04 · openalex publication_date 2015/11/04 · arxiv updated 2015/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We received a solution of the shadow problem in n-dimensional Euclidean space for a family of sets, constructing from any convex domain having nonempty interior with the help of parallel translations and homotheties. We find a number of balls with centers on the sphere, sufficient for giving a shadow in n-dimensional complex (hypercomplex) space.

Related

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• On the shadow problem and its generalizations to ellipsoids
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• Some remarks about system of balls that generate shadow at point
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