Brunn-Minkowski inequality for theta-convolution bodies via Ball's bodies

Alonso Gutiérrez, David (Universidad de Zaragoza) ; Javier Martín Goñi

Resumen: We 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.

Idioma: Inglés

DOI: 10.1007/s12220-023-01508-2

Año: 2024

Publicado en: JOURNAL OF GEOMETRIC ANALYSIS 34, 58 (2024), 1-15
ISSN: 1050-6926

Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-20R
Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-23R
Financiación: info:eu-repo/grantAgreement/ES/MCINN/PID2022-137294NB-I00

Tipo y forma: Article (Published version)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)