An existence result for a quantitative isoperimetric inequality in $\mathbb{R}^3$ involving the Hausdorff asymmetry
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914609888231424 |
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| author | Bove, Silvio Croce, Gisella Pisante, Giovanni |
| author_facet | Bove, Silvio Croce, Gisella Pisante, Giovanni |
| contents | We study the existence of an optimizer for a quantitative isoperimetric ratio $\mathcal{Q}_*$ in $\mathbb{R}^3$ involving the Hausdorff asymmetry. We prove that $\mathcal{Q}_*$ attains its minimum over the class $\mathcal{A}$ of convex bodies of fixed volume. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29046 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An existence result for a quantitative isoperimetric inequality in $\mathbb{R}^3$ involving the Hausdorff asymmetry Bove, Silvio Croce, Gisella Pisante, Giovanni Optimization and Control 49Q10, 52A40, 49Q20, 31A15 We study the existence of an optimizer for a quantitative isoperimetric ratio $\mathcal{Q}_*$ in $\mathbb{R}^3$ involving the Hausdorff asymmetry. We prove that $\mathcal{Q}_*$ attains its minimum over the class $\mathcal{A}$ of convex bodies of fixed volume. |
| title | An existence result for a quantitative isoperimetric inequality in $\mathbb{R}^3$ involving the Hausdorff asymmetry |
| topic | Optimization and Control 49Q10, 52A40, 49Q20, 31A15 |
| url | https://arxiv.org/abs/2605.29046 |