On isoperimetric local-Bollobás-Thomason inequalities
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915743714508800 |
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| author | Alías, Luis J. Merino, Bernardo González Gimeno, Beatriz Marín |
| author_facet | Alías, Luis J. Merino, Bernardo González Gimeno, Beatriz Marín |
| contents | We prove the following isoperimetric-type inequality: for every convex body $K$ in $\mathbb R^n$ and some $σ\subset[n]:=\{1,\dots,n\}$ there exists a suitable Hanner polytope $B_K$ with the same volume as $K$ and such that the volume of each of its orthogonal projections onto every subspace whose basis is formed by the canonical vectors $\{e_i:i\inτ\cup([n]\setminusσ)\}$, for every $τ\subseteqσ$, bounds from below the volume of the corresponding projections of $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15044 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On isoperimetric local-Bollobás-Thomason inequalities Alías, Luis J. Merino, Bernardo González Gimeno, Beatriz Marín Metric Geometry Functional Analysis We prove the following isoperimetric-type inequality: for every convex body $K$ in $\mathbb R^n$ and some $σ\subset[n]:=\{1,\dots,n\}$ there exists a suitable Hanner polytope $B_K$ with the same volume as $K$ and such that the volume of each of its orthogonal projections onto every subspace whose basis is formed by the canonical vectors $\{e_i:i\inτ\cup([n]\setminusσ)\}$, for every $τ\subseteqσ$, bounds from below the volume of the corresponding projections of $K$. |
| title | On isoperimetric local-Bollobás-Thomason inequalities |
| topic | Metric Geometry Functional Analysis |
| url | https://arxiv.org/abs/2601.15044 |