Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds

Ai Jun Li, Dongmeng Xi, Gaoyong Zhang

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)494-538
Number of pages45
JournalAdvances in Mathematics
Volume304
DOIs
StatePublished - Jan 2 2017

Fingerprint

Grassmann Manifold
Convex Body
Transform
Isoperimetric
Stefan Banach
Unit ball
Reverse
Norm

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds. / Li, Ai Jun; Xi, Dongmeng; Zhang, Gaoyong.

In: Advances in Mathematics, Vol. 304, 02.01.2017, p. 494-538.

Research output: Contribution to journalArticle

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