The dual Brunn–Minkowski theory for bounded Borel sets: Dual affine quermassintegrals and inequalities

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Dual Orlicz–Brunn–Minkowski theory: Dual Orlicz Lϕ affine and geominimal surface areas (2014, background): “The dual (Lp) BrunnMinkowski theory for star bodies received considerable attention, see [2, 4, 8, 12, 13, 14, 27, 33, 53] among others.”
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.”
The dual Minkowski problem for negative indices (2017, unknown): “Also see Gardner [14] and Schneider [38] for a detailed account.”
Existence of solutions to the even dual Minkowski problem (2018, background): “Quoting from Gardner, Hug & Weil [19]:“The dual Brunn-Minkowski theory can count among its successes the solution of the Busemann-Petty problem in [16], [20], [41], and [68].”