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15 January 2006 Isoperimetry of waists and local versus global asymptotic convex geometries
Roman Vershynin
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Duke Math. J. 131(1): 1-16 (15 January 2006). DOI: 10.1215/S0012-7094-05-13111-8

Abstract

If two symmetric convex bodies K and L both have nicely bounded sections, then the intersection of random rotations of K and L is also nicely bounded. For L being a subspace, this main result immediately yields the unexpected existence versus prevalence phenomenon: If K has one nicely bounded section, then most sections of K are nicely bounded. The main result represents a new connection between the local asymptotic convex geometry (study of sections of convex bodies) and the global asymptotic convex geometry (study of convex bodies as a whole). Our method relies on the recent isoperimetry of waists due to M. Gromov [G].

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Roman Vershynin. "Isoperimetry of waists and local versus global asymptotic convex geometries." Duke Math. J. 131 (1) 1 - 16, 15 January 2006. https://doi.org/10.1215/S0012-7094-05-13111-8

Information

Published: 15 January 2006
First available in Project Euclid: 15 December 2005

zbMATH: 1103.46008
MathSciNet: MR2219235
Digital Object Identifier: 10.1215/S0012-7094-05-13111-8

Subjects:
Primary: 46B07
Secondary: 52A20

Rights: Copyright © 2006 Duke University Press

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Vol.131 • No. 1 • 15 January 2006
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