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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2604.14000 |
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| _version_ | 1866917410773139456 |
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| author | Amato, Vincenzo Gavitone, Nunzia Sannipoli, Rossano |
| author_facet | Amato, Vincenzo Gavitone, Nunzia Sannipoli, Rossano |
| contents | In this paper, given a convex, bounded, open set $Ω\subset \mathbb{R}^n$ we prove a sharp inequality involving the Laplacian torsional rigidity and both the perimeter and the measure of the domain.
Our result generalizes to arbitrary dimensions the inequality established by Makai in the plane which, as conjectured in arXiv:2007.02549. Furthermore, we establish quantitative estimates that provide key insights into the geometric structure and the thickness of the underlying optimizing sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14000 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Makai inequality in higher dimensions: qualitative and quantitative aspects Amato, Vincenzo Gavitone, Nunzia Sannipoli, Rossano Analysis of PDEs Spectral Theory In this paper, given a convex, bounded, open set $Ω\subset \mathbb{R}^n$ we prove a sharp inequality involving the Laplacian torsional rigidity and both the perimeter and the measure of the domain. Our result generalizes to arbitrary dimensions the inequality established by Makai in the plane which, as conjectured in arXiv:2007.02549. Furthermore, we establish quantitative estimates that provide key insights into the geometric structure and the thickness of the underlying optimizing sequences. |
| title | The Makai inequality in higher dimensions: qualitative and quantitative aspects |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2604.14000 |