Symmetrization in geometry
Symmetrization in geometry
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几何对称
DOI：
10.1016/j.aim.2016.10.003
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发表时间：
2016
影响因子：
1.7
通讯作者：
P. Gronchi
中科院分区：
文献类型：
--
作者：
Gabriele Bianchi;Richard J. Gardner;P. Gronchi
引入了非对称化的概念，为凸集上的大多数对称化过程提供了一个方便的框架。介绍了非对称化的各种性质，并研究了它们之间的关系。给出了紧凸集的Steiner和Minkowski代数的新的表达式，它们之间具有对偶关系。施泰纳，闵可夫斯基和中央对称化，在自然属性，他们享有的特征，给出了例子，并表明，没有一个假设可以下降或显着削弱。其他熟悉的对称化，如施瓦茨对称化，进行了讨论，并介绍了几个新的。
The concept of ani-symmetrization is introduced, which provides a convenient framework for most of the familiar symmetrization processes on convex sets. Various properties ofi-symmetrizations are introduced and the relations between them investigated. New expressions are provided for the Steiner and Minkowski symmetrals of a compact convex set which exhibit a dual relationship between them. Characterizations of Steiner, Minkowski and central symmetrization, in terms of natural properties that they enjoy, are given and examples are provided to show that none of the assumptions made can be dropped or significantly weakened. Other familiar symmetrizations, such as Schwarz symmetrization, are discussed and several new ones introduced.