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arXiv · 2205.09096

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

Steven Hoehner·Jeff Ledford
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Abstract

Weighted cone-volume functionals are introduced for the convex polytopes in $\mathbb{R}^n$. 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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Steven Hoehner, Jeff Ledford. 2022-05-18. Extremal arrangements of points on the sphere for weighted cone-volume functionals. https://arxiv.org/abs/2205.09096

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