doi:10.1007/s12220-023-01508-2engAlonso Gutiérrez, DavidJavier Martín GoñiBrunn-Minkowski inequality for theta-convolution bodies via Ball's bodiesART-2024-136090We consider the problem of finding the best function ϕn : [0, 1] → R such that for any pair of convex bodies K, L ∈ Rn the following Brunn–Minkowski type inequality holds |K +θ L| 1n ≥ ϕn(θ )(|K| 1 n + |L| 1 n ), where K +θ L is the θ-convolution body of K and L. We prove a sharp inclusion of the family of Ball’s bodies of an α-concave function in its super-level sets in order to provide the best possible function in the range 3 4 n ≤ θ ≤ 1, characterizing the equality cases.2024http://zaguan.unizar.es/record/12977610.1007/s12220-023-01508-2http://zaguan.unizar.es/record/129776oai:zaguan.unizar.es:129776info:eu-repo/grantAgreement/ES/DGA/E48-20Rinfo:eu-repo/grantAgreement/ES/DGA/E48-23Rinfo:eu-repo/grantAgreement/ES/MICINN/PID2022-137294NB-I00JOURNAL OF GEOMETRIC ANALYSIS 34, 58 (2024), 1-15byhttps://creativecommons.org/licenses/by/4.0/deed.esinfo:eu-repo/semantics/openAccess