Volumes of subset Minkowski sums and the Lyusternik region
arXiv:2112.06518 · doi:10.1007/s00454-023-00606-w
Abstract
We begin a systematic study of the region of possible values of the volumes of Minkowski subset sums of a collection of compact sets in , 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.
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