非对称的$L_{p}$-径向差体

doi:10.12066/j.issn.1007-2861.2032

上海大学学报(自然科学版) ›› 2019, Vol. 25 ›› Issue (4): 493-501.doi: 10.12066/j.issn.1007-2861.2032

非对称的$L_{p}$-径向差体

齐继兵()

1.上海大学理学院,上海 200444
2. 合肥师范学院数学与统计学院, 合肥 230601

收稿日期:2017-10-26 出版日期:2019-08-30 发布日期:2019-09-04
通讯作者: 齐继兵 E-mail:qijibing@ahu.edu.cn
基金资助:
安徽省自然科学基金资助项目(1908085QA04)

Asymmetric $L_{p}$-radial difference bodies

Jibing QI()

1.College of Sciences, Shanghai University, Shanghai 200444
2. Department of Mathematics and Statistics, Hefei Normal University, Hefei 230601, China

Received:2017-10-26 Online:2019-08-30 Published:2019-09-04
Contact: Jibing QI E-mail:qijibing@ahu.edu.cn

摘要/Abstract

摘要：

定义了关于星体的非对称的 $L_{p}$-径向差体, 研究了其性质, 建立了关于非对称 $L_{p}$-径向差体的对偶均值积分的几个不等式. 作为其特例, 得到非对称$L_{p}$-径向差体体积的几个不等式.

关键词: 星体, 差体, 均值积分, 凸几何

Abstract:

The notion of asymmetric $L_{p}$-radial difference bodies about star bodies has been defined, and some of their properties have been studied. Some inequalities for dual quermassintegrals of asymmetric $L_{p}$-radial difference bodies have been established. In particular, some inequalities for the volumes of asymmetric $L_p$-radial difference bodies have been obtained.

Key words: star body, difference bodies, dual quermassintegrals, convex geometry

中图分类号:

O184

齐继兵. 非对称的$L_{p}$-径向差体[J]. 上海大学学报(自然科学版), 2019, 25(4): 493-501.

Jibing QI. Asymmetric $L_{p}$-radial difference bodies[J]. Journal of Shanghai University（Natural Science Edition）, 2019, 25(4): 493-501.

参考文献 22

[1]	Ludwig M . Minkowski valuations[J]. Trans Amer Math Soc, 2005,357:4191-4213.
[2]	Ludwig M . Intersection bodies and valuations[J]. Amer J Math, 2006,128:1409-1428.
[3]	Haberl C . $L_p$ intersection bodies[J]. Adv Math, 2008,217:2599-2624.
[4]	Haberl C, Schuster F E . General $L_p$ affine isoperimetric inequalities[J]. J Differential Geom, 2009,83:1-26.
[5]	Haberl C, Schuster F E . Asymmetric affine $L_p$ Sobolev inequalities[J]. J Funct Anal, 2009,257:641-658.
[6]	Haberl C, Schuster F E, Xiao J . An asymmetric affine P$\acute{\rm o}$lya-Szeg$\ddot{\rm o}$ principle[J]. Math Ann, 2012,352:517-542.
[7]	Weberndorfer M . Shadow systems of asymmetric $L_p$ zonotopes[J]. Adv Math, 2013,240:613-635.
[8]	Parapatits L . $SL(n)$-covariant $L_p$-Minkowski valuations[J]. J Lond Math Soc, 2014,89:397-414.
[9]	Parapatits L . $SL(n)$-contravariant $L_p$-Minkowski valuations[J]. Trans Amer Math Soc, 2014,366:1195-1211.
[10]	Schuster F E, Wannerer T . $GL(n)$ contravariant Minkowski valuations[J]. Trans Amer Math Soc, 2012,364:815-826.
[11]	Schuster F E, Weberndorfer M . Volume inequalities for asymmetric Wulff shapes[J]. J Differential Geom, 2012,92:263-283.
[12]	Wang W D, Wan X Y . Shephard type problems for general $L_p$-projection bodies[J]. Taiwan J Math, 2012,16:1749-1762.
[13]	Wang W D, Feng Y B . A general $L_p$-version of Petty's affine projection inequality[J]. Taiwan J Math, 2013,17:517-528.
[14]	Wang W D, Ma T Y . Asymmetric $L_p$-difference bodies[J]. Proc Amer Math Soc, 2014,142:2517-2527.
[15]	Wang W D . On inequalities for quermassintegrals and dual quermassintegrals of difference bodies[J]. Math Inequal Appl, 2014,17:41-48.
[16]	Feng Y B, Wang W D, Lu F H . Some inequalities on general $L_p$-centroid bodies[J]. Math Ineq Appl, 2015,18:39-49.
[17]	Schneider R. Convex bodies: the Brunn-Minkowski theory [M]. 2nd ed. Cambridge: Cambridge University Press, 2014.
[18]	Lutwak E . Intersection bodies and dual mixed volumes[J]. Adv Math, 1988,71:232-261.
[19]	Lutwak E . The Brunn-Minkowski-Firey theory: II. Affine and geominimal surface areas[J]. Adv Math, 1996,118:244-294.
[20]	Moszy$\acute{N}$ska M . Quotient star bodies, intersection bodies, and star duality[J]. J Math Anal Appl, 1999,232:45-60.
[21]	Wang W D, Leng G S . $L_ p$-dual mixed quermassintegrals[J]. Indian J Pure Appl Math, 2005,36:177-188.
[22]	李小燕, 何斌吾 . 对偶 Brunn-Minkowski-Firey 定理[J]. 数学杂志, 2005,25(3):545-548.

非对称的$L_{p}$-径向差体

Asymmetric $L_{p}$-radial difference bodies

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献 22

相关文章 6

编辑推荐

Metrics

本文评价

[1]	刘其霞. q-对偶Aleksandrov-Fenchel 不等式的稳定性[J]. 上海大学学报(自然科学版), 2013, 19(2): 154-159.
[2]	郭路军. p-余弦变换及其在凸几何分析中的应用[J]. 上海大学学报(自然科学版), 2012, 18(6): 601-605.
[3]	胡妍，蒋俊华. 星体的对偶0-加和L₀-对偶混合体积[J]. 上海大学学报(自然科学版), 2012, 18(2): 170-173.
[4]	吕松军;冷岗松. 星体的p-极曲率映象与p-仿射表面积[J]. 上海大学学报(自然科学版), 2008, 14(2): 148-151 .
[5]	潘东云;袁俊;冷岗松. 调和径向组合的对偶均质积分[J]. 上海大学学报(自然科学版), 2008, 14(1): 58-60 .
[6]	李雨红;袁俊;冷岗松. 星体的弦长积分[J]. 上海大学学报(自然科学版), 2006, 12(4): 394-398 .