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INEQUALITIES FOR MIXED INTERSECTION BODIES 被引量：3

INEQUALITIES FOR MIXED INTERSECTION BODIES
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摘要 In this paper, some properties of mixed intersection bodies are given, and inequalities from the dual Brunn-Minkowski theory (such as the dual Minkowski inequality, the dual Aleksandrov-Fenchel inequalities and the. dual Brunn-Minkowski inequalities) are established for mixed intersection bodies.
作者 YUANSHUFENG LENGGANGSONG
机构地区 DepartmentofMathematics DepartmentofMathematics
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2005年第3期423-436,共14页 数学年刊（B辑英文版）
基金 Project supported by the National Natural Science Foundation of China (No.10271071).
关键词 Star body Mixed intersection body Dual mixed volume Spherical radon transform 恒星体 最大交叉体 双重混合体积 球面氡转换 积分模型
分类号 O186.5 [理学—基础数学] P144.4 [天文地球—天体物理]
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参考文献28

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  • 2Bourgain, J. & Lindenstrauss, J., Projection Bodies, Geometric Aspects of Functional Analysis, Lecture Notes in Math. 1317, Springer, 1988, 250-270.
  • 3Busemann, H., A theorem on convex bodies of the Brunn-Minkowski type, Proc. Nat. Acad. Sci.,35(1949), 27-31.
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  • 6Gardner, R. J., Geometric Tomography, Cambridge University Press, New York, 1995.
  • 7Gardner, R. J., Intersection bodies and the Busemann-Petty problem, Trans. Amer. Math. Soc.,342(1994), 435-445.
  • 8Gardner, R. J., Koldobsky, A. & Schlumprecht, T., An analytic solution to the Busemann-Petty problem on sections of convex bodies, Ann. of Math., 149(1999), 691-703.
  • 9Hardy, G. H., Littlewood, J. E. & Polya, G., Inequalities, Cambridge Univ. Press, Cambridge, 1959.
  • 10Koldobsky, A., Intersection bodies and the Busemann-Petty problem, C. R. Ac ad. Sci. Paris Ser. I Math., 325(1997), 1181-1186.

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Chinese Annals of Mathematics,Series B
2005年 第3期

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