覆盖锥体和双锥体的泛函。

IF 1.6 3区数学 Q1 Mathematics

Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-07-24 DOI:10.1186/s13660-018-1785-9

Senlin Wu, Ke Xu

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引用次数: 8

摘要

使凸体K可以被γK的m个平移所覆盖的最小正数γ称为K(关于m)的覆盖泛函，用Γm(K)表示。凸体覆盖泛函的估计是宗传明攻击Hadwiger覆盖猜想定量方案的重要组成部分。给出了锥和双锥的覆盖泛函的估计，它们对于m和K的某些对是最优的。

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Covering functionals of cones and double cones.

The least positive number γ such that a convex body K can be covered by m translates of γK is called the covering functional of K (with respect to m), and it is denoted by $Γ_{m} (K)$ . Estimating covering functionals of convex bodies is an important part of Chuanming Zong's quantitative program for attacking Hadwiger's covering conjecture. Estimations of covering functionals of cones and double cones, which are best possible for certain pairs of m and K, are presented.

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来源期刊

Journal of Inequalities and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.30

自引率

6.20%

发文量

136

审稿时长

3 months

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.