Refinements of the Brunn-Minkowski inequality
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Universidad de Murcia
info
ISSN: 0944-6532
Año de publicación: 2014
Volumen: 21
Número: 3
Páginas: 727-743
Tipo: Artículo
Otras publicaciones en: Journal of Convex Analysis
Resumen
Brunn-Minkowski theorem says that Vol (1−λ)K +λL1/n ) for K, L convex bodies, is a concavefunction in λ, and assuming a common hyperplane projection of K and L, it was proved thatthe volume itself is concave. In this paper we study refinements of Brunn-Minkowski inequality,in the sense of ‘enhancing’ the exponent, either when a common projection onto an (n−k)-planeis assumed or for particular families of sets. In the first case, we show that the expected resultof concavity for the k-th root of the volume is not true, although other Brunn-Minkowski typeinequalities can be obtained under the (n − k)-projection hypothesis. In the second case, weshow that for p-tangential bodies, the exponent in Brunn-Minkowski inequality can be replacedby 1/p.