Lp-混合相交体

虞志刚

数学学报 ›› 2010, Vol. 53 ›› Issue (1) : 25-36.

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数学学报 ›› 2010, Vol. 53 ›› Issue (1) : 25-36. DOI: 10.12386/A2010sxxb0004
论文

Lp-混合相交体

    虞志刚
作者信息 +

Quasi-Lp-Mixed Intersection Bodies

    Zhi Gang YU
Author information +
文章历史 +

摘要

1988年, Lutwak 首次提出了相交体的概念.本文在相交体以及拟Lp-相交体的基础上,引入了拟Lp-混合相交体的概念.通过利用对偶Lp-混合均值积分理论和相关的不等式,给出了Lp型的Busemann相交不等式,建立了关于Lp径向组合和Lp-调和Blaschke组合的Brunn--Minkowski型不等式及其隔离形式, 并且探讨了拟Lp-混合相交体的单调性问题.

 

Abstract

In 1988, Lutwak first brought into being the concept of Intersection Bodies, based on which, complemented by that of Quasi-Lp-Intersection Bodies, the present paper proposes a new idea of Quasi Lp-mixed Intersection Bodies. With the help of the dual Lp-Mixed Quermassintegrals theory and some related inequalities, the paper gives the Lp-Busemann Intersetion Inequality, establishes some dual Brunn--Minkowski inequalities and their isolated forms for Lp-mixed intersection body about Lp-radial combination and Lp-harmonic Blaschke combination, as well as lodges a discussion on the problem of Quasi-Lp-mixed Intersection Bodies' monotonicity.

 

关键词

Lp-混合相交体 / 星体 / 对偶混合均值积分

Key words

quasi-Lp-mixed intersection bodies / star bodies / dual mixed quermassintegrals

引用本文

导出引用
虞志刚. Lp-混合相交体. 数学学报, 2010, 53(1): 25-36 https://doi.org/10.12386/A2010sxxb0004
Zhi Gang YU. Quasi-Lp-Mixed Intersection Bodies. Acta Mathematica Sinica, Chinese Series, 2010, 53(1): 25-36 https://doi.org/10.12386/A2010sxxb0004

参考文献


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基金

国家自然科学基金资助项目(10671117)

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