凸集对称化的算术调和平均不等式收紧与反转

IF 1.2 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics Pub Date : 2021-12-27 DOI:10.1142/s0219199722500456

René Brandenberg, Katherina von Dichter, Bernardo González Merino

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引用次数: 2

摘要

本文讨论了凸集C的四种对称:C和- C的交、调和和算术平均以及凸包。Firey的一个众所周知的结果表明，这些方法按照给定的顺序构建子集链。一方面，我们根据C的不对称性来确定膨胀因子，以逆转任何这些对称之间的包含。另一方面，我们加强了Firey证明的关系，并给出了这些因素在单纯形附近的稳定性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Tightening and reversing the arithmetic-harmonic mean inequality for symmetrizations of convex sets

This paper deals with four symmetrizations of a convex set C: the intersection, the harmonic and the arithmetic mean, and the convex hull of C and −C. A well-known result of Firey shows that those means build up a subset-chain in the given order. On the one hand, we determine the dilatation factors, depending on the asymmetry of C, to reverse the containments between any of those symmetrizations. On the other hand, we tighten the relations proven by Firey and show a stability result concerning those factors near the simplex.

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来源期刊

Communications in Contemporary Mathematics 数学-数学

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： With traditional boundaries between various specialized fields of mathematics becoming less and less visible, Communications in Contemporary Mathematics (CCM) presents the forefront of research in the fields of: Algebra, Analysis, Applied Mathematics, Dynamical Systems, Geometry, Mathematical Physics, Number Theory, Partial Differential Equations and Topology, among others. It provides a forum to stimulate interactions between different areas. Both original research papers and expository articles will be published.