Generalizations of the Busemann–Petty problem for sections of convex bodies

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Generalized intersection bodies (2005, methodology): “ion bodies in [Kol00]), and that the generalized k-codimensional problem is equivalent to whether all convex bodies in Rn are k-Busemann-Petty bodies. It was shown in [BZ98] (see also a correction in [RZ04]), and later in [Kol00], that the answer is negative for k < n − 3, but the cases k = n − 3”
The Busemann-Petty problem for arbitrary measures (2004, methodology): “Corollary 3 is a generalization of a result of Koldobsky ([K7], Theorem 8; see also [ RZ ]), where the case of n k = 3 and M = Bn 2 was considered.”
Divergence for s-concave and log concave functions (2013, background): “, [19]- [23], [29], [30], [34]- [48], [58], [62]- [67], [69], [72]), this theory is now a central part of modern convex geometry.”
R\'enyi Divergence and $L_p$-affine surface area for convex bodies (2011, unknown): “, [5], [7] - [11], [13], [14], [17] - [24], [26], [28], [31] - [34], [37], [38] - [46], [50]), is now a central part of modern convex geometry.”
Dual Orlicz-Brunn-Minkowski theory (2014, background): “See [1–3, 11–13,15,17,19,47,48,55] for more historical details about the Busemann–Petty problem.”