Asymptotic formulas for the diameter of sections of symmetric convex bodies

Journal of Functional Analysis

Volumn 223, Issue 1, 2005, Pages 86-108

  Giannopoulos, Apostolos ^a,d   Milman, Vitali D ^b   Tsolomitis, Antonis ^c  

^a UNIVERSITY OF CRETE   (Greece)

^b TEL AVIV UNIVERSITY   (Israel)

^c UNIVERSITY OF THE AEGEAN   (Greece)

^d UNIVERSITY OF ATHENS   (Greece)

Author keywords

Asymptotic formulas; Local theory of finite dimensional normed spaces; Random sections of convex bodies

Indexed keywords

EID: 17844399813     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2004.10.006     Document Type: Article

References (19)

1. S. Artstein Proportional concentration phenomena on the sphere Israel J. Math. 132 2002 337-358
2. n, Lecture Notes in Mathematics, vol. 1317 1988 84-106
3. M. Gromov Isoperimetry of waists and concentration of maps Geom. Funct. Anal 13 2003 178-215
4. A. Giannopoulos, V.D. Milman, On the diameter of proportional sections of a symmetric convex body, International Mathematics Research Notices, vol. 1 1997 5-19
5. A. Giannopoulos V.D. Milman How small can the intersection of a few rotations of a symmetric convex body be? C. R. Acad. Sci. Paris 325 1997 389-393
6. A. Giannopoulos V.D. Milman Mean width and diameter of proportional sections of a symmetric convex body J. Reine Angew. Math. 497 1998 113-139
7. A. Litvak V.D. Milman G. Schechtman Averages of norms and quasi-norms Math. Ann. 312 1998 95-124
8. V.D. Milman Geometrical inequalities and mixed volumes in the local theory of Banach spaces Astérisque 131 1985 373-400
9. V.D. Milman, Random subspaces of proportional dimension of finite dimensional normed spaces: Approach through the isoperimetric inequality, Lecture Notes in Mathematics, vol. 1166, 1985, pp. 106-115.
10. V.D. Milman, Spectrum of a position of a convex body and linear duality relations, Israel Mathematical Conference Proceedings (IMCP), vol. 3, Festschrift in Honor of Professor I. Piatetski-Shapiro (Part II), Weizmann Science Press of Israel 1990, pp. 151-162.
11. V.D. Milman, Some applications of duality relations, Lecture Notes in Mathematics, vol. 1469, 1991, pp. 13-40.
12. V.D. Milman, G. Schechtman, Asymptotic theory of finite-dimensional normed spaces, Lecture Notes in Mathematics, vol. 1200, 1986.
13. V.D. Milman G. Schechtman Global versus local asymptotic theories of finite-dimensional normed spaces Duke Math. J. 90 1997 73-93
14. P. Mankiewicz N. Tomczak-Jaegermann Geometry of families of random projections of symmetric convex bodies Geom. Funct. Anal. 11 2001 1282-1326
15. G. Pisier, The volume of convex bodies and Banach space geometry, Cambridge Tracts in Mathematics, vol. 94, 1989.
16. A. Pajor N. Tomczak-Jaegermann Subspaces of small codimension of finite dimensional Banach spaces Proc. Amer. Math. Soc. 97 1986 637-642
17. N. Tomczak-Jaegermann Banach-Mazur distances and Finite Dimensional Operator Ideals 1988 Longman New York
18. R. Vershynin, Concentration of measure on the sphere: Small values, preprint.
19. R. Vershynin, Isoperimetry of waists and local versus global asymptotic convex geometries, preprint (with an appendix by M. Rudelson and R. Vershynin).