Brunn–Minkowski inequalities for variational functionals and related problems

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The Minkowski problem for the torsional rigidity (2008, methodology): “For all the other examples of functionals mentioned before, including the torsional rigidity, (9) and (10) are valid; for the details we refer the reader to [4] and the literature quoted therein.”
Quermassintegrals of quasi-concave functions and generalized Prékopa–Leindler inequalities (2012, background): “As further examples of functionals satisfying a Brunn–Minkowski inequality, let us mention the p-capacity of convex bodies in Rn for 1 ≤ p < n (with α = 1 n−p , see [12,17]), the first non-trivial eigenvalue of the Laplacian with the Dirichlet boundary condition (with α = −2, see [13]) and other sim”