The log-Brunn-Minkowski inequality
The log-Brunn-Minkowski inequality
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DOI：
10.1016/j.aim.2012.07.015
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发表时间：
2012-10
影响因子：
1.7
通讯作者：
K. Böröczky;E. Lutwak;Deane Yang;Gaoyong Zhang
中科院分区：
文献类型：
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作者：
K. Böröczky;E. Lutwak;Deane Yang;Gaoyong Zhang
对于原点对称的凸体（即，有限维Banach空间的单位球），证明了存在一类强于经典Brunn-Minkowski不等式的不等式和一类强于经典Minkowski混合体积不等式的不等式.它表明，这两个家庭的不平等是“等价的”，一旦这些不平等的建立，其他必须遵循的后果。所有的不等式都是对平面凸体成立的。
For origin-symmetric convex bodies (i.e., the unit balls of finite dimensional Banach spaces) it is conjectured that there exist a family of inequalities each of which is stronger than the classical Brunn–Minkowski inequality and a family of inequalities each of which is stronger than the classical Minkowski mixed-volume inequality. It is shown that these two families of inequalities are “equivalent” in that once either of these inequalities is established, the other must follow as a consequence. All of the conjectured inequalities are established for plane convex bodies.