Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 22
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Li, Ai-Jun and Huang, Qingzhong 2016. The dual Loomis–Whitney inequality. Bulletin of the London Mathematical Society, Vol. 48, Issue. 4, p. 676.

    DU, CHANGMIN GUO, LUJUN and LENG, GANGSONG 2015. Volume inequalities for Orlicz mean bodies. Proceedings - Mathematical Sciences, Vol. 125, Issue. 1, p. 57.

    Shen, Rulin and Zhu, Baocheng 2015. L p Harmonic radial combinations of star bodies. Journal of Inequalities and Applications, Vol. 2015, Issue. 1,

    Hu, Junfang 2014. Stability in the Shephard problem. Indagationes Mathematicae, Vol. 25, Issue. 3, p. 454.

    JIN, HAILIN and YUAN, SHUFENG 2014. A sharp Rogers–Shephard type inequality for Orlicz-difference body of planar convex bodies. Proceedings - Mathematical Sciences, Vol. 124, Issue. 4, p. 573.

    Li, Ai-Jun 2014. The generalization of Minkowski problems for polytopes. Geometriae Dedicata, Vol. 168, Issue. 1, p. 245.

    Liu, Shuai and He, Binwu 2014. The Pólya-Szegö Principle and the Anisotropic Convex Lorentz-Sobolev Inequality. The Scientific World Journal, Vol. 2014, p. 1.

    Xi, Dongmeng Jin, Hailin and Leng, Gangsong 2014. The Orlicz Brunn–Minkowski inequality. Advances in Mathematics, Vol. 260, p. 350.

    Zhu, Baocheng Zhou, Jiazu and Xu, Wenxue 2014. Dual Orlicz–Brunn–Minkowski theory. Advances in Mathematics, Vol. 264, p. 700.

    Weberndorfer, Manuel 2013. Shadow systems of asymmetric zonotopes. Advances in Mathematics, Vol. 240, p. 613.

    ZHU, BAOCHENG LI, NI and ZHOU, JIAZU 2013. BRUNN–MINKOWSKI TYPE INEQUALITIES FOR Lp MOMENT BODIES. Glasgow Mathematical Journal, Vol. 55, Issue. 02, p. 391.

    Huang, Qingzhong and He, Binwu 2012. On the Orlicz Minkowski Problem for Polytopes. Discrete & Computational Geometry, Vol. 48, Issue. 2, p. 281.

    Zhu, Guangxian 2012. The Orlicz centroid inequality for star bodies. Advances in Applied Mathematics, Vol. 48, Issue. 2, p. 432.

    Chen, Fangwei Zhou, Jiazu and Yang, Congli 2011. On the reverse Orlicz Busemann–Petty centroid inequality. Advances in Applied Mathematics, Vol. 47, Issue. 4, p. 820.

    Haberl, Christoph Lutwak, Erwin Yang, Deane and Zhang, Gaoyong 2010. The even Orlicz Minkowski problem. Advances in Mathematics, Vol. 224, Issue. 6, p. 2485.

    Lutwak, Erwin Yang, Deane and Zhang, Gaoyong 2010. Orlicz projection bodies. Advances in Mathematics, Vol. 223, Issue. 1, p. 220.

    Wang, Weidong 2010. On reverses of the L p -Busemann-Petty centroid inequality and its applications. Wuhan University Journal of Natural Sciences, Vol. 15, Issue. 4, p. 292.

    Weidong, Wang and Gangsong, Leng 2010. Inequalities of the quermassintegrals for the Lp-projection body and the Lp-centroid body. Acta Mathematica Scientia, Vol. 30, Issue. 1, p. 359.

    Yu, Wuyang 2009. Equivalence of Some Affine Isoperimetric Inequalities. Journal of Inequalities and Applications, Vol. 2009, Issue. 1, p. 981258.

    Wang, Wei Dong and Leng, Gang Song 2007. The Petty Projection Inequality for L p -Mixed Projection Bodies. Acta Mathematica Sinica, English Series, Vol. 23, Issue. 8, p. 1485.


On the reverse Lp–busemann–petty centroid inequality

  • Stefano Campi (a1) and Paolo Gronchi (a2)
  • DOI:
  • Published online: 01 February 2010

The volume of the Lp-centroid body of a convex body K ⊂ ℝd is a convex function of a time-like parameter when each chord of K parallel to a fixed direction moves with constant speed. This fact is used to study extrema of some affine invariant functionals involving the volume of the Lp-centroid body and related to classical open problems like the slicing problem. Some variants of the Lp-Busemann-Petty centroid inequality are established. The reverse form of these inequalities is proved in the two-dimensional case.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[CG]S. Campi and P. Gronchi , The Lp-Busemann-Petty centroid inequality body, Adv. Math. 167 (2002), 128141.

[FR]I. Fáry and L. Rédei . Der zentralsymmetrische Kern und die zentralsymmetrische Hüllc von konvexen Körpern, Math. Ann. 122 (1950), 205220.

[J1]F. John . Polar correspondence with respect to convex regions, Duke Math. J. 3 (1937), 355369.

[LM]J. Lindenstrauss and V. D. Milman , Local theory of normed spaces and convexity, Handbook of Convex Geometry (P. M. Gruber and J. M. Wills , eds.), North-Holland, Amsterdam, 1993, pp. 11491220.

[MP]V. D. Milman and A. Pajor . Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space. Geometric Aspects of Functional Analysis (J. Lindenstrauss and V. D. Milman , eds.), vol. 1376, Springer Lecture Notes in Math., 1989, 64104.

[P1]C. M. Petty . Centroid surfaces. Pacific J. Math. 11 (1961), 15351547.

[P2]C. M. Petty , Ellipsoids, Convexity and its Applications (P. M. Gruber and J. M. Wills , eds.). Birkhäuser, Basel, 1983, pp. 264276.

[RT]C. A. Rogers and S. J. Taylor , The analysis of additive set functions in Euclidean space, Acta Math. 101 (1959), 273302.

[Sc]F. Scheck , Mechanics, Springer-Verlag, Berlin Heidelberg, 1990.

[Sh]G. C. Shephard , Shadow systems of convex bodies, Israel J. Math. 2 (1964), 229–36.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
Please enter your name
Please enter a valid email address
Who would you like to send this to? *