For origin-symmetric convex bodies, weighted dual quermassintegrals satisfy an L_p Brunn-Minkowski inequality with exponent p/q under natural radial log-concavity conditions on the weight.
Cordero-Erausquin and A
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Proves dimensional Brunn-Minkowski inequality for even log-concave measures with c_n ≥ c/(n^3 ln n) and shows Γ_n ≈ n for maximal functional perimeter of isotropic log-concave measures.
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$L_p$ Brunn-Minkowski inequality for weighted dual quermassintegrals
For origin-symmetric convex bodies, weighted dual quermassintegrals satisfy an L_p Brunn-Minkowski inequality with exponent p/q under natural radial log-concavity conditions on the weight.
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Functional perimeter and the dimensional Brunn-Minkowski inequality for log-concave measures
Proves dimensional Brunn-Minkowski inequality for even log-concave measures with c_n ≥ c/(n^3 ln n) and shows Γ_n ≈ n for maximal functional perimeter of isotropic log-concave measures.