f-Divergence for convex bodies
Abstract
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 Lp affine surface area from the Lp Brunn Minkowski theory are special cases of f-divergences.
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