Translative containment measure and symmetric mixed isohomothetic inequalities
Translative containment measure and symmetric mixed isohomothetic inequalities
复制标题
平移遏制措施和对称混合等位不等式
DOI：
10.1007/s11425-015-5074-5
复制
发表时间：
2015-12-01
影响因子：
1.4
通讯作者：
Zhou JiaZu
中科院分区：
文献类型：
--
作者：
Luo Miao;Xu WenXue;Zhou JiaZu
首先研究凸域K（0）包含或被包含在另一凸域K（1）的位似副本中的平移包含测度，即，给定欧氏平面a“e（2）中面积分别为A（0），A（1）的两个凸域K（0），K（1），是否存在平移T使得t（TK（1））aS，K（0）或t（TK（1））aS积分K（0）（t > 0）？利用积分几何中Poincar和Blaschke的平移运动学公式，估计了对称混合同位相似亏损σ（2）（K（0），K（1））a千分之一A（01）（2）- A（0）A（1），其中A（01）是K（0）和K（1）的混合面积.我们得到了K 0包含或包含在t（TK（1））中的一个充分条件。得到了一些Bonnesen型对称混合同构不等式和反向Bonnesen型对称混合同构不等式。当其中一个区域为圆盘时，得到的这些对称混合同位映射不等式称为Bonnesen型等参不等式和逆Bonnesen型等参不等式.作为直接结果，我们得到了一些不等式，加强了已知的Minkowski不等式的混合区域和Bonnesen-Blaschke-弗兰德斯不等式。
We first investigate the translative containment measure for convex domain K (0) to contain, or to be contained in, the homothetic copy of another convex domain K (1), i.e., given two convex domains K (0), K (1) of areas A (0), A (1), respectively, in the Euclidean plane a"e(2), is there a translation T so that t(TK (1)) aS, K (0) or t(TK (1)) aS integral K (0) for t > 0? Via the translative kinematic formulas of Poincar, and Blaschke in integral geometry, we estimate the symmetric mixed isohomothetic deficit sigma(2)(K (0),K (1)) a parts per thousand A (01) (2) - A (0) A (1), where A (01) is the mixed area of K (0) and K (1). We obtain a sufficient condition for K0 to contain, or to be contained in, t(TK (1)). We obtain some Bonnesen-style symmetric mixed isohomothetic inequalities and reverse Bonnesen-style symmetric mixed isohomothetic inequalities. These symmetric mixed isohomothetic inequalities obtained are known as Bonnesen-style isopermetric inequalities and reverse Bonnesen-style isopermetric inequalities if one of domains is a disc. As direct consequences, we obtain some inequalities that strengthen the known Minkowski inequality for mixed areas and the Bonnesen-Blaschke-Flanders inequality.