Applications of new affine invariant for polytopes

摘要

To study the Schneider's projection problem,Lutwak,Yang and Zhang recently introduced a new affine invariant functional U(P) for convex polytopes in R^n. In the paper,we obtain the analytic expression of the affine-invariant U(P) defined on a specific subclass of origin-symmetric convex polytopes in R^n and give an application of U(P) to the L_p-Minkowski problem.