Volumes of subset Minkowski sums and the Lyusternik region
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866929272189353984 |
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| author | Barthe, Franck Madiman, Mokshay |
| author_facet | Barthe, Franck Madiman, Mokshay |
| contents | 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 $\mathbb{R}^d$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_06518 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Volumes of subset Minkowski sums and the Lyusternik region Barthe, Franck Madiman, Mokshay Combinatorics Metric Geometry 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 $\mathbb{R}^d$, 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. |
| title | Volumes of subset Minkowski sums and the Lyusternik region |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2112.06518 |