Lp-混合仿射表面积的不等式

朱先阳

数学学报 ›› 2013, Vol. 56 ›› Issue (2) : 279-288.

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数学学报 ›› 2013, Vol. 56 ›› Issue (2) : 279-288. DOI: 10.12386/A2013sxxb0029
论文

Lp-混合仿射表面积的不等式

    朱先阳
作者信息 +

Some Inequalities for Lp-Mixed Affine Surface Area

    Xian Yang ZHU
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文章历史 +

摘要

引入了第i个Lp-混合仿射表面积和Lp-极曲率像概念, 建立了几个与新概念及Lp-质心体、p-Blaschke体有关的不等式,获得了关于Lp-混合仿射表面积的Blaschke-Santaló类不等式. 所获结果能得到经典对偶Urysohn不等式的广义形式.

Abstract

In this paper, the concepts of the i th Lp-mixed affine surface area and Lp-polar curvature images are introduced, some new inequalities connecting these new notions with Lp-centroid bodies and p-Blaschke bodies are established. Moreover, a Blaschke-Santaló type inequality for Lp-mixed affine surface area is established. Our results also imply a generalization of the class dual Urysohn inequalities.

关键词

Lp-混合仿射表面积 / Lp-极曲率像 / p-Blaschke线性组合 / Lp-质心体

Key words

Lp-mixed affine surface area / Lp-polar curvature images / p-Blaschke linear combination / Lp-centroid body

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朱先阳. Lp-混合仿射表面积的不等式. 数学学报, 2013, 56(2): 279-288 https://doi.org/10.12386/A2013sxxb0029
Xian Yang ZHU. Some Inequalities for Lp-Mixed Affine Surface Area. Acta Mathematica Sinica, Chinese Series, 2013, 56(2): 279-288 https://doi.org/10.12386/A2013sxxb0029

参考文献

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基金

国家自然科学基金资助项目(11161024);江西省自然科学基金资助项目(2010GZC0115)

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