星体的Green-Osher型不等式及其应用

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中图分类号：0186.5 文献标志码：A

Green-Osher Type Inequality for Star Bodies and Its Applications

DING Jie， ZHANG De-yan， YUAN Ming-yang （School of Mathematics and Statistics，Huaibei Normal University，Huaibei 235OOo，China）

Abstract：To compare the squared norm of the dual relative Steiner polynomial roots with the relative radial function for star bodies P and Q ，a nonnegative real number r0 was defined by the roots of the j -th dual relative Steiner polynomial. Then analogously to the method of proving Green-Osher inequality for planar convex bodies， a GreenOsher type inequality for star bodies in Rn was deduced. Based on this result，two dual Minkowski type inequalities were obtained.

Keywords： star body;Steiner polynomial; Green-Osher inequality；Minkowski inequality

设 γ 是一条平面简单闭曲线，若记 L 和 A 为γ的周长和所围区域面积，则经典的等周不等式陈述了L2-4πA≥0 ，当且仅当γ为圆周时等号成立。（剩余7635字）