Relative entropy of cone measures and L p centroid bodies

Grigoris Paouris, Elisabeth M. Werner

Research output: Contribution to journalArticlepeer-review

75 Scopus citations

Abstract

Let K be a convex body in ℝ n. We introduce a new affine invariant, which we call Ω K, that can be found in three different ways: as a limit of normalized L p-affine surface areas;as the relative entropy of the cone measure of K and the cone measure of K°;as the limit of the volume difference of K ̊ and L p-centroid bodies. We investigate properties of Ω K and of related new invariant quantities. In particular, we show new affine isoperimetric inequalities and we show an 'information inequality' for convex bodies.

Original languageEnglish (US)
Pages (from-to)253-286
Number of pages34
JournalProceedings of the London Mathematical Society
Volume104
Issue number2
DOIs
StatePublished - Feb 2012

Bibliographical note

Funding Information:
The first author was partially supported by an NSF grant. The second author was partially supported by an NSF grant, an FRG-NSF grant and a BSF grant.

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