VOLUME INEQUALITIES FOR SETS ASSOCIATED WITH CONVEX BODIES
VOLUME INEQUALITIES FOR SETS ASSOCIATED WITH CONVEX BODIES
复制标题
与凸体相关的集合的体积不等式
DOI：
10.1142/9789812774644_0001
复制
发表时间：
2006
影响因子：
0.6
通讯作者：
P. Gronchi
中科院分区：
文献类型：
--
作者：
S. Campi;P. Gronchi
本文研究凸体体积与投影体、L-质心体及其极体积的不等式。例子是Blaschke-Santalo不等式，Petty和Zhang投影不等式，Busemann-Petty不等式。其他同类不等式尚处于探索阶段。凸体的特殊连续运动的应用为这一问题提供了一种一般的方法。得到了Lutwak证明的一类依赖于参数p ≥ 1的不等式，其中p = 1，p = 2.
This paper deals with inequalities for the volume of a convex body and the volume of the projection body, the L-centroid body, and their polars. Examples are the Blaschke-Santalo inequality, the Petty and Zhang projection inequalities, the Busemann-Petty inequality. Other inequalities of the same type are still at the stage of conjectures. The use of special continuous movements of convex bodies provides a general approach to this subject. A family of inequalities, depending on a parameter p ≥ 1 and proved by Lutwak for p = 1 and p = 2, is obtained.