An isomorphic version of the slicing problem

Journal of Functional Analysis

Volumn 218, Issue 2, 2005, Pages 372-394

  Klartag, B ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Alexandrov Fenchel inequalities; Convex bodies; Hyperplane sections; The slicing problem

Indexed keywords

EID: 11044236927     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2004.05.003     Document Type: Article

References (24)

1. S. Artstein, V. Milman, S. Szarek, Duality of metric entropy, Ann. Math., to appear.
2. n Studia Math. 88 1988 69-84
3. K.M. Ball, Normed spaces with a weak-Gordon-Lewis property, Proceedings of Functional Analysis, University of Texas and Austin (1987-1989), Lecture Notes in Mathematics, Vol. 1470, Springer, Berlin, 1991, pp. 36-47.
4. Bastero J. Bernués J. Peña A. An extension of Milman's reverse Brunn-Minkowski inequality Geom. Funct. Anal. 5 3 1995 572-581
5. Borell C. Convex set functions in d-space Period. Math. Hungar. 6 2 1975 111-136
6. Bourgain J. On high-dimensional maximal functions associated to convex bodies Amer. J. Math. 108 6 1986 1467-1476
7. J. Bourgain, On the distribution of polynomials on high dimensional convex sets, Geometric Aspects of Functional Analysis (1989-1990), Lecture Notes in Mathematics, Vol. 1469, Springer, Berlin, 1991, pp. 127-137.
8. J. Bourgain, B. Klartag, V. Milman, Symmetrization and isotropic constants of convex bodies, in Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics, to appear.
9. n Invent. Math. 88 2 1987 319-340
10. Carl B. Entropy numbers, s-numbers and eigenvalue problems J. Funct. Anal. 41 1981 290-306
11. Dar S. Remarks on Bourgain's problem on slicing of convex bodies, Geometric aspects of functional analysis Oper. Theory: Adv. Appl. 77 1995 61-66
12. Gromov M. Milman V.D. Generalization of the spherical isoperimetric inequality to uniformly convex Banach spaces Composition Math. 62 1987 263-282
13. p Forum Math. 6 5 1994 617-635
14. B. Klartag, V.D. Milman, Rapid Steiner symmetrization of most of a convex body and the slicing problem, Combin. Probab. Comput., special issue in honor of Béla Bollobás, to appear.
15. König H. Meyer M. Pajor A. The isotropy constants of the Schatten classes are bounded Math. Ann. 312 4 1998 773-783
16. Milman V.D. Inégalité de Brunn-Minkowski inverse et applications à le théorie locale des espaces normés C.R. Acad. Sci. Paris Ser. I 302 1986 25-28
17. V.D. Milman, Some applications of duality relations, Geometric Aspects of Functional Analysis (1989-1990), Lecture Notes in Mathematics, Vol. 1469, Springer, Berlin, 1991, pp. 127-137.
18. V.D. Milman, A. Pajor, Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space, Geometric Aspects of Functional Analysis (1987-1988), Lecture Notes in Mathematics, Vol. 1376, Springer, Berlin, 1989, pp. 64-104.
19. Milman V.D. Pajor A. Entropy and Asymptotic Geometry of Non-Symmetric Convex bodies Adv. in Math. 152 2 2000 314-335
20. V.D. Milman, G. Schechtman, Asymptotic Theory of Finite-Dimensional Normed Spaces, Lecture Notes in Mathematics, Vol. 1200, Springer, Berlin, 1986.
21. G. Paouris, On the isotropic constant of non-symmetric convex bodies, Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics, Vol. 1745, Springer, Berlin, 2000, pp. 239-243.
22. G. Pisier, The volume of convex bodies and Banach space geometry, Cambridge Tracts in Mathematics, Vol. 94, Cambridge University Press, Cambridge, 1997.
23. Santaló L.A. An affine invariant for convex bodies of n-dimensional space Portugal. Math. 8 1949 155 161 (in Spanish)
24. R. Schneider, Convex bodies: The Brunn-Minkowski theory, Encyclopedia of Mathematics and its Applications, Vol.44, Cambridge University Press, Cambridge, 1993.