凸体Minkowski不等式的改进

赵长健

数学学报 ›› 2013, Vol. 56 ›› Issue (5) : 687-692.

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PDF(340 KB)
数学学报 ›› 2013, Vol. 56 ›› Issue (5) : 687-692. DOI: 10.12386/A2013sxxb0068
论文

凸体Minkowski不等式的改进

    赵长健
作者信息 +

On Improvements of Minkowski Inequality for Convex Bodies

    Chang Jian ZHAO
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文章历史 +

摘要

本文改进了凸体体积差的Minkowski不等式,获得了凸体混合体积差函数的Minkowski型不等式的加强形式,给出了凸体混合体积差函数的新的下界估计.

Abstract

In the paper, some sharp Minkowski-type inequalities for volume differences are established. Our results provide new estimates on inequalities of these types.

关键词

体积差函数 / 对偶体积差函数 / 混合p-均值积分 / Minkowski型不等式

Key words

volume difference function / dual volume difference function / mixed pquermassintegrals / Minkowski inequality

引用本文

导出引用
赵长健. 凸体Minkowski不等式的改进. 数学学报, 2013, 56(5): 687-692 https://doi.org/10.12386/A2013sxxb0068
Chang Jian ZHAO. On Improvements of Minkowski Inequality for Convex Bodies. Acta Mathematica Sinica, Chinese Series, 2013, 56(5): 687-692 https://doi.org/10.12386/A2013sxxb0068

参考文献

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[6] Lutwak E., The Brunn-Minkowski-Firey theory I: Mixed volumes and the Minkowski problem, J. Diff. Geom., 1993, 38: 131-150.
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[8] Mitrinović D. S., Analytic Inequalities, Springer-Verlag, Berlin, New York, 1970.
[9] Schneider R., Boundary Structure and Curvature of Convex Bodies, Contributions to Geometry, Birkhäuster, Basel, 1979: 13-59.
[10] Schneider R., Convex Bodies: The Brunn-Minkowski Theory, Cambridge Univ. Press, New York, 1993.
[11] Zhao C., Cheung W., On p-quermassintegral differences function, Proc. Indian Acad. Sci. Math. Sci., 2006, 116: 221-231.

基金

国家自然科学基金资助项目(10971205)

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