On local Liakopoulos-Meyer type inequalities and their functional counterparts
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917119127453696 |
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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 provide a functional Rogers-Shephard type inequality for log-concave functions on $\mathbb R^n$ and any $1$-reducible $s$-cover of $[n]$. As a consequence, we derive a sharp local Liakopoulos-Meyer type inequality for $n$-dimensional convex bodies and $1$-reducible $s$-covers of any $σ\subset[n]$, solving a question studied by Brazitikos, Giannopoulos, Liakopoulos in [14] as well as Alonso-Gutiérrez, Bernués, Brazitikos, Carbery in [3]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_02761 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On local Liakopoulos-Meyer type inequalities and their functional counterparts Alías, Luis J. Merino, Bernardo González Gimeno, Beatriz Marín Metric Geometry Functional Analysis We provide a functional Rogers-Shephard type inequality for log-concave functions on $\mathbb R^n$ and any $1$-reducible $s$-cover of $[n]$. As a consequence, we derive a sharp local Liakopoulos-Meyer type inequality for $n$-dimensional convex bodies and $1$-reducible $s$-covers of any $σ\subset[n]$, solving a question studied by Brazitikos, Giannopoulos, Liakopoulos in [14] as well as Alonso-Gutiérrez, Bernués, Brazitikos, Carbery in [3]. |
| title | On local Liakopoulos-Meyer type inequalities and their functional counterparts |
| topic | Metric Geometry Functional Analysis |
| url | https://arxiv.org/abs/2512.02761 |