On the volume of sums of anti-blocking bodies
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929509679235072 |
|---|---|
| author | Manui, Auttawich Ndiaye, Cheikh Saliou Zvavitch, Artem |
| author_facet | Manui, Auttawich Ndiaye, Cheikh Saliou Zvavitch, Artem |
| contents | We study inequalities on the volume of Minkowski sum in the class of anti-blocking bodies. We prove analogues of Plünnecke-Ruzsa type inequality and V. Milman inequality on the concavity of the ratio of volumes of bodies and their projections. We also study Firey $L_p-$sums of anti-blocking bodies and prove Plünnecke-Ruzsa type inequality; V. Milman inequality and Roger-Shephard inequality. The sharp constants are provided in all of those inequalities, for the class of anti-blocking bodies. Finally, we extend our results to the case of unconditional product measures with decreasing density. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14214 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the volume of sums of anti-blocking bodies Manui, Auttawich Ndiaye, Cheikh Saliou Zvavitch, Artem Metric Geometry Functional Analysis 52A20, 52A21 We study inequalities on the volume of Minkowski sum in the class of anti-blocking bodies. We prove analogues of Plünnecke-Ruzsa type inequality and V. Milman inequality on the concavity of the ratio of volumes of bodies and their projections. We also study Firey $L_p-$sums of anti-blocking bodies and prove Plünnecke-Ruzsa type inequality; V. Milman inequality and Roger-Shephard inequality. The sharp constants are provided in all of those inequalities, for the class of anti-blocking bodies. Finally, we extend our results to the case of unconditional product measures with decreasing density. |
| title | On the volume of sums of anti-blocking bodies |
| topic | Metric Geometry Functional Analysis 52A20, 52A21 |
| url | https://arxiv.org/abs/2409.14214 |