The Sine Transform of Isotropic Measures

被引：21
作者：
Maresch, Gabriel [1 ]
Schuster, Franz E. [1 ]
机构：
[1] Vienna Univ Technol, Vienna, Austria
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2012年 / 2012卷 / 04期
基金：
奥地利科学基金会;
关键词：
VOLUME INEQUALITIES; YOUNGS-INEQUALITY; CONVEX-BODIES; SUBSPACES; ENTROPY;
D O I：
10.1093/imrn/rnr035
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Sharp isoperimetric inequalities for the sine transform of even isotropic measures are established. The corresponding reverse inequalities are obtained in an asymptotically optimal form. These new inequalities have direct applications to strong volume estimates for convex bodies from data about their sections or projections.
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收藏
页码：717 / 739
页数：23
相关论文
共 53 条
  • [1] Ball K, 2001, HANDBOOK OF THE GEOMETRY OF BANACH SPACES, VOL 1, P161, DOI 10.1016/S1874-5849(01)80006-1
  • [2] SHADOWS OF CONVEX-BODIES
    BALL, K
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 327 (02) : 891 - 901
  • [3] BALL K, 1991, J LOND MATH SOC, V44, P351
  • [4] BALL K, 1989, LECT NOTES MATH, V1376, P251
  • [5] Entropy of spherical marginals and related inequalities
    Barthe, F.
    Cordero-Erausquin, D.
    Maurey, B.
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2006, 86 (02): : 89 - 99
  • [6] Barthe F, 2004, LECT NOTES MATH, V1850, P53
  • [7] On a reverse form of the Brascamp-Lieb inequality
    Barthe, F
    [J]. INVENTIONES MATHEMATICAE, 1998, 134 (02) : 335 - 361
  • [8] An extremal property of the mean width of the simplex
    Barthe, F
    [J]. MATHEMATISCHE ANNALEN, 1998, 310 (04) : 685 - 693
  • [9] Brascamp-Lieb inequalities and convexity
    Barthe, F
    [J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 324 (08): : 885 - 888
  • [10] The Brascamp-Lieb inequalities: Finiteness, structure and extremals
    Bennett, Jonathan
    Carbery, Anthony
    Christ, Michael
    Tao, Terence
    [J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2007, 17 (05) : 1343 - 1415
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