Sharp affine isoperimetric inequalities for the volume decomposition functionals of polytopes
Sharp affine isoperimetric inequalities for the volume decomposition functionals of polytopes
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多面体体积分解泛函的精确仿射等周不等式
DOI：
10.1016/j.aim.2021.107902
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发表时间：
2021-10
影响因子：
1.7
通讯作者：
Yude Liu;Qiang Sun;Ge Xiong
中科院分区：
文献类型：
--
作者：
Yude Liu;Qiang Sun;Ge Xiong
根据任意n个P的单位外法向量张成的空间的维数，将R n中多边形P的体积泛函V n的n次幂分解为n次齐次多项式。建立了R 3中这些体积分解泛函的一组新的尖锐仿射等周不等式，从本质上表征了R n中多边形的几何和代数结构。
The nth power of the volume functional V n of polytopes P in R n, according to dimensions of the spaces spanned by any n unit outer normal vectors of P, is decomposed into n homogeneous polynomials of degree n. A set of new sharp affine isoperimetric inequalities for these volume decomposition functionals in R 3 are established, which essentially characterize the geometric and algebraic structures of polytopes.