The Cramer-Rao inequality for star bodies

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OPERATIONS BETWEEN SETS IN GEOMETRY (2012, unknown): “See, for example, [9], [22], [23], [29], [30], [31], [32], [33], and [34].”
The log-Brunn-Minkowski inequality (2012, unknown): “[5,8–12,16,18,22–30,32–55,58,62–65,67–69]).”
The even Orlicz-Minkowski problem (2010, unknown): “[1–5, 7–10, 12, 13, 15–22, 25–39, 41–44, 47, 49, 50, 52–55, 58, 60–63, 65–68]).”
Relative entropy of cone measures and Lp centroid bodies (2009, background): “We denote by |K| the n-dimensional volume of the convex body K and by K◦ = {y ∈ Rn : 〈x, y〉 1} the polar body of K.”
The logarithmic Minkowski problem (2012, unknown): “From this and the deﬁnition of cone-volume measure we have where in going from the second to the third line we changed variables x = ρ ˜ K ( u ) u , for u ∈ S m − 1 , and used the fact that (see e.g., [43], Lemma 2).”
Fisher information and matrix-valued valuations (2011, methodology): “Lutwak, Yang, and Zhang [37] introduced a new ellipsoid associated with convex sets and showed in [39] that this LYZ ellipsoid corresponds to the Fisher information ellipsoid defined by the Fisher information matrix.”
Divergence for s-concave and log concave functions (2013, background): “Applications are given in the theory of convex bodies.”