关于对偶Steiner多项式的根的注记

Notes on roots of the dual Steiner polynomial

受凸体的Steiner多项式的启发,定义了星体的对偶Steiner多项式,并利用对偶Aleksandrov-Fenchel不等式讨论了对偶Steiner多项式的根.进而,得到了关于对偶Steiner多项式的根的一些不等式,这些不等式恰好是关于Steiner多项式的根的不等式的对偶形式.

Motivated by the Steiner polynomial for convex bodies, the dual Steiner polynomial for star bodies is defined. Furthermore, roots of the dual Steiner polynomial are discussed by applying the dual AleksandrovFenchel inequality, and some inequalities involving roots of the dual Steiner polynomial are obtained, where these inequalities are just dual forms of those of the Steiner polynomial.