M-estimates for isotropic convex bodies and their Lq-centroid bodies

Apostolos Giannopoulos; Emanuel Milman

doi:10.1007/978-3-319-09477-9__13

M-estimates for isotropic convex bodies and their L_q-centroid bodies

Apostolos Giannopoulos, Emanuel Milman

Technion - Israel Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

Let K be a centrally-symmetric convex body in Rⁿ and let ||· || be its induced norm on Rⁿ. We show that if K 2 ⊇ Bⁿ₂ then: (Formula presented) where M(K) = ∫S^n-1 ||x|| da(x) is the mean-norm, C> 0 is a universal constant, and^V-_k (K) denotes the minimal volume-radius of a k-dimensional orthogonal projection of K. We apply this result to the study of the mean-norm of an isotropic convex body K in Rⁿ and its Lq-centroid bodies. In particular, we show that if K has isotropic constant L_K then: (Formula presented).

Original language	English
Title of host publication	Geometric Aspects of Functional Analysis
Subtitle of host publication	Israel Seminar (GAFA) 2011–2013
Pages	159-182
Number of pages	24
DOIs	https://doi.org/10.1007/978-3-319-09477-9__13 https://doi.org/10.1007/978-3-319-09477-9_13
State	Published - 2014

Publication series

Name	Lecture Notes in Mathematics
Publisher	Springer Verlag
Volume	2116

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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Cite this

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