f-Divergence for Convex Bodies

Elisabeth M. Werner

Research output: Chapter in Book/Report/Conference proceedingChapter

5 Scopus citations


We introduce f-divergence, a concept from information theory and statistics, for convex bodies in ℝn. We prove that f-divergences are SL(n) invariant valuations and we establish an affine isoperimetric inequality for these quantities. We show that generalized affine surface area and in particular the Lpaffine surface area from the LpBrunn Minkowski theory are special cases of f-divergences.

Original languageEnglish (US)
Title of host publicationAsymptotic Geometric Analysis
Subtitle of host publicationProceedings of the Fall 2010 Fields Institute Thematic Program
EditorsMonika Ludwig, Vladimir Pestov, Vitali Milman, Nicole Tomczak-Jaegermann
Number of pages15
StatePublished - 2013

Publication series

NameFields Institute Communications
ISSN (Print)1069-5265

Bibliographical note

Funding Information:
Prof. Werner’s work was partially supported by an NSF grant, a FRG-NSF grant and a BSF grant.


  • Affine surface area
  • Relative entropy
  • f-divergence


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