# Generalization of the spherical isoperimetric inequality to uniformly convex Banach spaces

Compositio Mathematica (1987)

- Volume: 62, Issue: 3, page 263-282
- ISSN: 0010-437X

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topGromov, M., and Milman, V. D.. "Generalization of the spherical isoperimetric inequality to uniformly convex Banach spaces." Compositio Mathematica 62.3 (1987): 263-282. <http://eudml.org/doc/89842>.

@article{Gromov1987,

author = {Gromov, M., Milman, V. D.},

journal = {Compositio Mathematica},

keywords = {concentration of measure on spheres of uniformly convex Banach spaces; isoperimetric inequality; non-invariant measures; Brunn-Minkowski theorem; localized Brunn's theorem; lower exponential bound on the dimension; symmetric map; Lipschitz constant},

language = {eng},

number = {3},

pages = {263-282},

publisher = {Martinus Nijhoff Publishers},

title = {Generalization of the spherical isoperimetric inequality to uniformly convex Banach spaces},

url = {http://eudml.org/doc/89842},

volume = {62},

year = {1987},

}

TY - JOUR

AU - Gromov, M.

AU - Milman, V. D.

TI - Generalization of the spherical isoperimetric inequality to uniformly convex Banach spaces

JO - Compositio Mathematica

PY - 1987

PB - Martinus Nijhoff Publishers

VL - 62

IS - 3

SP - 263

EP - 282

LA - eng

KW - concentration of measure on spheres of uniformly convex Banach spaces; isoperimetric inequality; non-invariant measures; Brunn-Minkowski theorem; localized Brunn's theorem; lower exponential bound on the dimension; symmetric map; Lipschitz constant

UR - http://eudml.org/doc/89842

ER -

## References

top- [AM] D. Amir and V.D. Milman: A quantitative finite-dimensional Krivine Theorem, Israel J. Math. (1985) to appear. Zbl0612.46021MR788067
- [GM1] M. Gromov and V.D. Milman: A topological application of the isoperimetric inequality. Amer. J. Math.105 (1983) 843-854. Zbl0522.53039MR708367
- [GM2] M. Gromov and V.D. Milman: Brunn Theorem and a concentration of volume phenomena for symmetric convex bodies. Geometric Aspects of Functional Analysis, Seminar Notes, Tel Aviv (1983-1984). Zbl0953.52500MR827283
- [H] H. Hadwiger: Vorlesungen Über Inhalt: Oberfläche und Isoperimetrie, Springer-Verlag (1957). Zbl0078.35703MR102775
- [P] G. Pisier: Remarques sur un Résultat non publié de B. Maurey, Séminaire d'Analyse Fonctionnelle (1980- 1981) Exp. V. Zbl0491.46017MR659306
- [S] J.J. Schäffer: Inner diameter, perimeter, and girth of spheres. Math. Ann.173 (1967) 59-82. Zbl0152.12405MR218875
- [R] V.A. Rohlin: On the fundamental ideas of measure theory. Mat. Sbornic, N.S.25 (67), (1949), 107-150 (Russian). (Amer. Math. Soc. Translation71, 55pp., (1952)).
- [BZ] Y.D. Burago and V.A. Zalgaler: Geometrical Inequalities. Leningrad, " Nauka" (1980). Zbl0436.52009

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