On the Lp Intersection Body
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摘要: 通过利用Brunn-Minkowski-Firey混合体积及对偶混合体积理论,研究了Lp-截面体和对偶混合体积的相互关系,建立了关于正规化Lp-径向加及Lp-径向线性组合的Lp-截面体的Brunn-Minkowski形不等式及其隔离形式,且获得了算子Ip的一些性质.
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关键词:
- 星体 /
- Lp-截面体 /
- 性质 /
- Brunn-Minkowski不等式
Abstract: By using Brunn-Minkowski-Firey mixed volume theory and dual mixed volume theory, associated with Lp intersection body and dual mixed volume, some dual Brunn-Minkowski inequalities and their isolate forms are established for Lp intersection body about the normalized Lp radial addition and Lp radial linear combination. Some properties of operator Ip are given.-
Key words:
- star body /
- Lp intersection body /
- property /
- Brunn-Minkowski inequality
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[1] Lutwak E.Intersection bodies and dual mixed volume[J].Adv Math,1988,71(2):232-261. doi: 10.1016/0001-8708(88)90077-1 [2] Gardner R J.Geometry Tomography[M].New York:Cambridge University Press,1995. [3] Gardner R J,Giannopoulos A A.p-Cross-section bodies[J].Indiana Univ Math J,1999,48(2):593-613. [4] Haberl C,Ludwig M.A characterization of Lp intersection bodies[J].International Mathematics Research Notices,Article ID 10548,2006,1-29. [5] Yaskin V,Yaskina M.Centeriod bodies and comparison of volume[J].Indiana Univ Math J,2006,55(3):1175-1194. doi: 10.1512/iumj.2006.55.2761 [6] Campi S,Gronchi P.The Lp-Busemann-Petty centroid inequakity[J].Adv Math,2002,167(1):128-141. doi: 10.1006/aima.2001.2036 [7] Lutwak E,Yang D,Zhang G.Lp affine isoperimetric inequalities[J].J Differential Geom,2000,56(1):111-132. [8] Lutwak E,Zhang G.Blaschke-Santaló inequalities[J],J Differential Geom,1997,47(1):1-16. [9] Grinberg E,Zhang G.Convolutions, transforms, and convex bodies[J].Proc London Math Soc,1999,78(3):77-115. doi: 10.1112/S0024611599001653 [10] Yu W,Wu D,Leng G.Qusai Lp-intersection bodies[J].Acta Math Sinica,2007,23(11):1937-1948. doi: 10.1007/s10114-007-0958-0 [11] Schneider R.Convex Bodies:The Brunn-Minkowski Theory[M].Cambridge:Cambridge University Press,1993. [12] Hardy G H,Littlewood J E,Polya G.Inequalities[M].Cambridge:Cambridge University Press,1959. [13] Lutwak E.The Brunn-Minkowski-Firy theory Ⅱ:affine and geominimal surface areas[J].Adv Math,1996,118(2):244-294. doi: 10.1006/aima.1996.0022 [14] Wang W,Leng G.Lp-dual mixed quermassintegrals[J].Pure Appl Math,2005,36(4):177-188.
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