Extremal arrangements of points on the sphere for weighted cone-volume functionals

2022/05/18 by Hoehner, Steven, Ledford, Jeff
#52A40 (Primary) 52A38 #52B11 #52C99 (Secondary) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2205.09096

Abstract

Weighted cone-volume functionals are introduced for the convex polytopes in ℝⁿ. For these functionals, geometric inequalities are proved and the equality conditions are characterized. A variety of corollaries are derived, including extremal properties of the regular polytopes involving the L_p surface area. Some applications to crystallography and quantum theory are also presented.

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