Connections between the LYZ functionals and volume decomposition functionals of polytopes
摘要
The volume decomposition functionals that were recently posed in Liu et al. (Adv Math 389:107902, 2021) to study the affine isoperimetric problem of polytopes, are shown to be uniquely represented as linear combinations of certain products of the LYZ functionals, which were originally introduced in Lutwak et al. (Trans Am Math Soc 353:1767–1779, 2001) to attack the longstanding Schneider projection problem in convex geometry.