The Existence of a Convex Polyhedron with Respect to the Constrained Vertex Norms

Supanut Chaidee and Kokichi Sugihara
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Supanut Chaidee: Advanced Research Center for Computational Simulation, Department of Mathematics, Faculty of Science, Chiang Mai University, 239 Huaykaew Road, Suthep District, Muang, Chiang Mai 50200, Thailand
Kokichi Sugihara: Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan

Mathematics, 2020, vol. 8, issue 4, 1-13

Abstract: Given a set of constrained vertex norms, we proved the existence of a convex configuration with respect to the set of distinct constrained vertex norms in the two-dimensional case when the constrained vertex norms are distinct or repeated for, at most, four points. However, we proved that there always exists a convex configuration in the three-dimensional case. In the application, we can imply the existence of the non-empty spherical Laguerre Voronoi diagram.

Keywords: convex polyhedron; convex configuration; spherical Laguerre Voronoi diagram (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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