Bonnesen-Style Symmetric Mixed Isoperimetric Inequality
Bonnesen-Style Symmetric Mixed Isoperimetric Inequality
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DOI：
10.1007/978-4-431-55215-4_9
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Wenxue Xu;Jiazu Zhou;Baocheng Zhu
中科院分区：
文献类型：
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作者：
Wenxue Xu;Jiazu Zhou;Baocheng Zhu
对于欧氏平面R2中的凸域Ki（i= 0，1）（内部非空的紧凸集）.分别用Ai和Piarea和circum-perimeter表示。对称混合等周亏损为。本文给出了一些Bonnesen型对称混合不等式，即形式为的不等式，其中是一个几何意义的非负不变量且为零当且仅当K 0和K1都是圆的.我们还得到了一些反向Bonnesen型对称混合不等式。这些不等式是已知几何不等式的自然推广，例如已知的经典等周不等式。
For convex domainsKi(i= 0, 1) (compact convex sets with non-empty interiors) in the Euclidean planeR2. Denote byAiandPiareas and circum-perimeters, respectively. The symmetric mixed isoperimetric deficit is. In this paper, we give some Bonnesen-style symmetric mixed inequalities, that is, inequalities of the form, whereis a non-negative invariant of geometric significance and vanishes if and only if bothK0andK1are discs. We also obtain some reverse Bonnesen-style symmetric mixed inequalities. Those inequalities are natural generalizations of known geometric inequalities, such as the known classical isoperimetric inequality.