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 language||English (US)|
|Title of host publication||Asymptotic Geometric Analysis|
|Subtitle of host publication||Proceedings of the Fall 2010 Fields Institute Thematic Program|
|Editors||Monika Ludwig, Vladimir Pestov, Vitali Milman, Nicole Tomczak-Jaegermann|
|Number of pages||15|
|State||Published - 2013|
|Name||Fields Institute Communications|
Bibliographical noteFunding 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