The first variation of the total mass of log-concave functions and related inequalities

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More on logarithmic sums of convex bodies (2014, background): “In [5], a necessary and sufficient condition was discovered (the planar case was treated by Stancu [42] [43]; see also [6] for other applications of the cone-volume measure and [8] for a possible functional generalization of the classical Minkowski problem).”
Valuations on Convex Functions (2017, background): “Moreover, classical functionals for convex sets including the intrinsic volumes have been extended to the space of quasi-concave functions in [7] and [28] (see also [9, 18]).”