Volumes of subset Minkowski sums and the Lyusternik region (original) (raw)

We begin a systematic study of the region of possible values of the volumes of Minkowski subset sums of a collection of M compact sets in R d , which we call the Lyusternik region, and make some first steps towards describing it. Our main result is that a fractional generalization of the Brunn-Minkowski-Lyusternik inequality conjectured by Bobkov et al. (2011) holds in dimension 1. Even though Fradelizi et al. (2016) showed that it fails in general dimension, we show that a variant does hold in any dimension. Content