论文标题
重量锥体功能的球体上的极端排列
Extremal arrangements of points on the sphere for weighted cone-volume functionals
论文作者
论文摘要
在$ \ mathbb {r}^n $中引入了加权锥体功能。对于这些功能，证明了几何不平等现象，并表征了平等条件。得出了各种推论，包括涉及$ L_P $表面积的常规多型的极端特性。还提出了一些用于晶体学和量子理论的应用。
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.
