凸体的Steiner对称化的两个定理
Two Theorems of Steiner Symmetrization on Convex Bodies
DOI: 10.12677/PM.2017.75047, PDF, HTML, XML,  被引量 下载: 1,420  浏览: 2,731 
作者: 孙丽英*：陕西师范大学，数学与信息科学学院，陕西 西安
关键词: 凸体；Steiner对称化；Minkowski对称；超平面；Convex Body； Steiner Symmetrization； Minkowski Symmetrization； Hyperplane
摘要: 本文研究Steiner对称化在凸体上的充分条件。首先，我们根据Steiner对称化的性质，例如：保体积、保凸性、单调性、表面积减小等，构造一个凸体的变换 。其次，我们依据 满足的条件及Steiner对称化的概念，证明出 为凸体上的Steiner对称化，并且得到两个类似的推论。本文最后构造出了Steiner对称化的两个充分条件。
Abstract: In this paper, we mainly study sufficient conditions for Steiner symmetrization on convex bodies. Firstly, according to the properties of Steiner symmetrization, such as volume-preserving, convexity-preserving, monotonicity, surface area reduction and so on, we constructed a transformation on convex bodies. Secondly, in accordance to Steiner symmetrization’s characterization and concept, we proved that is Steiner symmetrization and came up with two homologous corollaries. Finally, we obtained two sufficient conditions for Steiner symmetrization.
文章引用：孙丽英. 凸体的Steiner对称化的两个定理[J]. 理论数学, 2017, 7(5): 368-372. https://doi.org/10.12677/PM.2017.75047

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