The Brunn-Minkowski inequality for p-capacity of convex bodies

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Sharp convex Lorentz–Sobolev inequalities (2011, unknown): “For more information on L p variational capacity, see [16,21,54].”
The p-capacitary Orlicz–Hadamard variational formula and Orlicz–Minkowski problems (2017, background): “with equality if and only if Ω and Ω1 are homothetic (see [3, 8, 11]).”
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”
Brunn–Minkowski inequalities for variational functionals and related problems (2005, background): “These results have been extended in [3] to the logarithmic capacity (or transfinite 27 diameter) in dimension n = 2, in [11] to the p-capacity, p > 1, and in [9] to the n-dimensional counterpart of the logarithmic capacity.”