Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds

Ai Jun Li; Dongmeng Xi; Gaoyong Zhang

doi:10.1016/j.aim.2016.09.007

Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds

Ai Jun Li, Dongmeng Xi, Gaoyong Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The L_p cosine transform on Grassmann manifolds naturally induces finite dimensional Banach norms whose unit balls are origin-symmetric convex bodies in Rⁿ. Reverse isoperimetric type volume inequalities for these bodies are established, which extend results from the sphere to Grassmann manifolds.

Original language	English (US)
Pages (from-to)	494-538
Number of pages	45
Journal	Advances in Mathematics
Volume	304
DOIs	https://doi.org/10.1016/j.aim.2016.09.007
State	Published - Jan 2 2017

Keywords

Ball–Barthe inequality
Cosine transform
Cross measure
Grassmann manifold
Isotropic measure
Mass transportation
Reverse isoperimetric inequality
Volume inequality

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2016.09.007

Cite this

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title = "Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds",

abstract = "The Lp cosine transform on Grassmann manifolds naturally induces finite dimensional Banach norms whose unit balls are origin-symmetric convex bodies in Rn. Reverse isoperimetric type volume inequalities for these bodies are established, which extend results from the sphere to Grassmann manifolds.",

keywords = "Ball–Barthe inequality, Cosine transform, Cross measure, Grassmann manifold, Isotropic measure, Mass transportation, Reverse isoperimetric inequality, Volume inequality",

author = "Li, {Ai Jun} and Dongmeng Xi and Gaoyong Zhang",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2017",

month = jan,

day = "2",

doi = "10.1016/j.aim.2016.09.007",

language = "English (US)",

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journal = "Advances in Mathematics",

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T1 - Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds

AU - Li, Ai Jun

AU - Xi, Dongmeng

AU - Zhang, Gaoyong

PY - 2017/1/2

Y1 - 2017/1/2

N2 - The Lp cosine transform on Grassmann manifolds naturally induces finite dimensional Banach norms whose unit balls are origin-symmetric convex bodies in Rn. Reverse isoperimetric type volume inequalities for these bodies are established, which extend results from the sphere to Grassmann manifolds.

AB - The Lp cosine transform on Grassmann manifolds naturally induces finite dimensional Banach norms whose unit balls are origin-symmetric convex bodies in Rn. Reverse isoperimetric type volume inequalities for these bodies are established, which extend results from the sphere to Grassmann manifolds.

KW - Ball–Barthe inequality

KW - Cosine transform

KW - Cross measure

KW - Grassmann manifold

KW - Isotropic measure

KW - Mass transportation

KW - Reverse isoperimetric inequality

KW - Volume inequality

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SP - 494

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JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds

Abstract

Keywords

ASJC Scopus subject areas

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