关于投影公式的一个注记

A Note on Projection Formula

凸体的混合体积理论提供了统一处理各种不同的重要的几何量的方法,比如体积和表面积等.在处理关于这些几何量的问题时广义柯西投影公式经常被使用.该文先给出了广义柯西投影公式的一个新证明,证明只使用了Minkowski定理和一些简单的计算,因此比原证明更为简单.A.Giannopoulos给出了一个几何不等式,该不等式的证明可看为广义柯西投影公式的一个应用.

The theory of mixed volumes provides a unified treatment of various important metric quantities in geometry such as volume and surface area. The generalized Cauchy projection formula is frequently used in dealing with problems concerning geometric quantities. In this paper, a new proof of the generalized Cauchy projection formulas is presented. We use only the Minkowski theory and some easy calculations, therefore is simpler compared to the original proof. Giannopoulos＇ geometric inequality can be viewed as an application of the generalized Cauchy projection formula.