Lp-对偶混合均质积分

王卫东, 马统一

数学学报 ›› 2012, Vol. 55 ›› Issue (6) : 1111-1118.

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数学学报 ›› 2012, Vol. 55 ›› Issue (6) : 1111-1118. DOI: 10.12386/A2012sxxb0107
论文

Lp-对偶混合均质积分

    王卫东1, 马统一2
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On the Lp-Dual Mixed Quermassintegrals

    Wei Dong WANG1, Tong Yi MA2
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摘要

结合星体的Lp-调和径向组合,王卫东和冷岗松于2005年介绍了Lp-对偶混合均质积分的概念.给出了这个概念 在一般线性变换下的一个性质,证明了关于这个概念的两个不等式,并利用这个概念给出了Lp-混合质心体的一个特征.

Abstract

Associated with the Lp-harmonic radial combination of star bodies, Wang and Leng in 2005 introduced the notion of Lp-dual mixed quermassintegrals. In this paper, we prove a property of the Lp-dual mixed quermassintegrals under linear transformation. Further, two inequalities for this notion are obtained. Finally, as the application of this notion, we give a characterization of the Lp-mixed centroid body.

关键词

Lp-调和径向组合 / Lp-对偶混合均质积分 / 对偶均质积分 / Lp-混合质心体

Key words

Lp-harmonic radial combination / Lp-dual mixed quermassintegrals / dual quermassintegrals / Lp-mixed centroid body

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王卫东, 马统一. Lp-对偶混合均质积分. 数学学报, 2012, 55(6): 1111-1118 https://doi.org/10.12386/A2012sxxb0107
Wei Dong WANG, Tong Yi MA. On the Lp-Dual Mixed Quermassintegrals. Acta Mathematica Sinica, Chinese Series, 2012, 55(6): 1111-1118 https://doi.org/10.12386/A2012sxxb0107

参考文献

[1] Firey W. J., Polar means of convex bodies and a dual to the Brunn-Minkowski theorem, Canad. J. Math.,1961, 13(2): 444-453.
[2] Firey W. J., Mean cross-section measures of harmonic means of convex bodies, Pacific J. Math., 1961, 11(6):1263-1266.
[3] Lutwak E., The Brunn-Minkowski-Firey theory II: affine and geominimal surface areas, Adv. Math., 1996,118(2): 244-294.
[4] Wang W. D., Leng G. S., Lp-dual mixed quermassintegrals, Indian J. Pure Appl. Math., 2005, 36(4): 177-188.
[5] Wang W. D., Leng G. S., A correction to our paper “Lp-dual mixed quermassintegrals”, Indian J. PureAppl. Math., 2007, 38(6): 609.
[6] Lutwak E., Dual mixed volumes, Pacific J. Math., 1975, 58(3): 531-538.
[7] Gardner R. J., Geometric Tomography, Second ed., Cambridge Univ. Press, Cambridge, 2006.
[8] Schneider R., Convex Bodies: The Brunn-Minkowski Theory, Cambridge Univ. Press, Cambridge, 1993.
[9] Lutwak E., Zhang G. Y., Blaschke-Santaló inequalities, J. Differential Geom., 1997, 47(1): 1-16.
[10] Lutwak E., Yang D., Zhang G. Y., Lp affine isoperimetric inequalities, J. Differential Geom., 2000, 56(1):111-132.
[11] Campi S., Grochi P., The Lp-Busemann-Petty centroid inequality, Adv. Math., 2002, 167(1): 128-141.
[12] Campi S., Grochi P., On the reverse Lp-Busemann-Petty centroid inequality, Mathematika, 2002, 49(1):1-11.
[13] Wang W. D., Lu F. H., Leng G. S., A type of monotonicity on the Lp centroid body and Lp projection body,Math. Ine. Appl., 2005, 8(4): 735-742.
[14] Wang W. D., Leng G. S., Some inequalities for the new body Γ?pK, Acta Mathematica Sinica, ChineseSeries, 2006, 49(6): 1327-1334.
[15] Wang W. D., Leng G. S., On the monotonicity of Lp-centroid bodies J. Sys. Sci. & Math. Sci., 2008, 28(2):154-162.
[16] Wang W. D., Leng G. S., Lu F. H., Brunn-Minkowski inequality for the quermassintegrals and dual quermassintegralsof Lp-projection bodies, Chinese Annals of Mathematics (in Chinese), 2008, 29(2): 209-220.
[17] Hardy G. H., Littlewood J. E., Pölya G., Inequalities, Cambridge University Press, Cambridge, 1959.

基金

国家自然科学基金资助项目(11161019); 三峡大学自然科学基金项目
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