Hlawka Type-1和Type-2之间的相互作用
Interactions between Hlawka Type-1 and Type-2 Quantities
摘要：
经典的Hlawka不等式与凸几何中的zonotopes和zerotopes有着深刻的联系，并与Minkowski空间有着密切的联系。引入Hlawka Type-1和Type-2量，并建立它们之间的Hlawka型关系，它连接了大量不同的Hlawka不等式的变体，如Minkowski空间未来锥上的Serre反向Hlawka不等式，Ressel关于阿贝尔群上次可加函数的Hlawka不等式，以及Takahasi等人的积分类似。我们宣布了几个增强的结果，如度量函数的幂的Hlawka不等式。特别地，我们给出了与Serre的一个工作有关的二次型的Hlawka不等式的完整的研究。
英文摘要：
The classical Hlawka inequality possesses deep connections with zonotopes and zonoids in convex geometry, and has been related to Minkowski space. We introduce Hlawka Type-1 and Type-2 quantities, and establish a Hlawka-type relation between them, which connects a vast number of strikingly different variants of the Hlawka inequalities, such as Serre's reverse Hlawka inequality in the future cone of the Minkowski space, the Hlawka inequality for subadditive function on abelian group by Ressel, and the integral analogs by Takahasi et al. Besides, we announce several enhanced results, such as the Hlawka inequality for the power of measure function. Particularly, we give a complete study of the Hlawka inequality for quadratic form which relates to a work of Serre.
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