论文标题
标准飞机的等量仪不平等
Isoperimetric Inequalities in Normed Planes
论文作者
论文摘要
经典的等法不等式可以扩展到一般规范平面。在欧几里得平面中，可以根据某些单数集的签名区域来计算等术不等式中的缺陷。在本文中，我们考虑了零件单位球和相应的可允许曲线类别的规范平面。对于这种可接受的曲线，将单数组定义为在对称和恒定宽度可允许曲线的子空间中的投影。在这种情况下，我们获得了一些改进的等值不平等，其相等性在对称或恒定宽度曲线中。
The classical isoperimetric inequality can be extended to a general normed plane. In the Euclidean plane, the defect in the isoperimetric inequality can be calculated in terms of the signed areas of some singular sets. In this paper we consider normed planes with smooth by parts unit balls and the corresponding class of admissible curves. For such an admissible curve, the singular sets are defined as projections in the subspaces of symmetric and constant width admissible curves. In this context, we obtain some improved isoperimetric inequalities whose equality hold for symmetric or constant width curves.
