A stability result for mean width of Lp-centroid bodies

Advances in Mathematics

Volumn 214, Issue 2, 2007, Pages 865-877

  Fleury, B ^a   Guedon O ^a   Paouris, G ^b  

^a SORBONNE UNIVERSITÉ   (France)

^b UFR des Sciences et Technologie   (France)

Author keywords

Concentration hypothesis; Lp centroid bodies; Reverse H lder inequality; Variance hypothesis

Indexed keywords

EID: 34447319149     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2007.03.008     Document Type: Article

References (21)

1. Anttila M., Ball K., and Perissinaki I. The central limit problem for convex bodies. Trans. Amer. Math. Soc. 355 12 (2003) 4723-4735
2. n. Studia Math. 88 1 (1988) 69-84
3. p-norms of polynomials. Geometric Aspects of Functional Analysis. Lecture Notes in Math. vol. 1745 (2000), Springer, Berlin 27-35
4. S.G. Bobkov, On isoperimetric constants for log-concave probability distributions, Geometric Aspects of Functional Analysis, Springer, Berlin, 2006, in press
5. Borell C. Complements of Lyapunov's inequality. Math. Ann. 205 (1973) 323-331
6. Bourgain J., and Lindenstrauss J. Projection bodies. Geometric Aspects of Functional Analysis (1986/1987). Lecture Notes in Math. vol. 1317 (1988), Springer, Berlin 250-270
7. Brehm U., and Voigt J. Asymptotics of cross sections for convex bodies. Beiträge Algebra Geom. 41 2 (2000) 437-454
8. Giannopoulos A. Notes on isotropic convex bodies, Institute of Mathematics, Polish Academy of Sciences, Warsaw (2003). http://users.uoa.gr/~apgiannop/isotropic-bodies.ps
9. Gordon Y. Gaussian processes and almost spherical sections of convex bodies. Ann. Probab. 16 1 (1988) 180-188
10. Groemer H. Geometric Applications of Fourier Series and Spherical Harmonics (1996), Cambridge Univ. Press, Cambridge
11. Kannan R., Lovász L., and Simonovits M. Isoperimetric problems for convex bodies and a localization lemma. Discrete Comput. Geom. 13 3-4 (1995) 541-559
12. Klartag B. A central limit theorem for convex sets. Invent. Math. 168 1 (2007) 91-131
13. p-spaces. Proc. Amer. Math. Soc. 122 (1994) 207-212
14. Litvak A.E., Milman V.D., and Schechtman G. Averages of norms and quasi-norms. Math. Ann. 312 1 (1998) 95-124
15. Lutwak E., and Zhang G. Blaschke-Santaló inequalities. J. Differential Geom. 47 1 (1997) 1-16
16. p affine isoperimetric inequalities. J. Differential Geom. 56 1 (2000) 111-132
17. Milman V.D. A new proof of A. Dvoretzky's theorem on cross-sections of convex bodies. Funktsional. Anal. i Prilozhen. 5 4 (1971) 28-37 (in Russian)
18. Milman V.D., and Schechtman G. Asymptotic Theory of Finite-Dimensional Normed Spaces. Lecture Notes in Math. vol. 1200 (1986), Springer, Berlin
19. 2-estimates for linear functionals on zonoids. Geometric Aspects of Functional Analysis. Lecture Notes in Math. vol. 1807 (2003), Springer, Berlin 211-222
20. Paouris G. Concentration of mass in convex bodies. Geom. Funct. Anal. 16 5 (2006) 1021-1049
21. Richards D.St.P. Positive definite symmetric functions on finite dimensional spaces. 1. Applications of the Radon transform. J. Multivariate Anal. 19 (1986) 280-298