Shape optimization under width constraint: the Cheeger constant and the torsional rigidity
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914413941882880 |
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| author | Bogosel, Beniamin |
| author_facet | Bogosel, Beniamin |
| contents | In this article it is shown that the equilateral triangle maximizes the Cheeger constant and minimizes the torsional rigidity among shapes having a fixed minimal width. The proof techniques use direct comparisons with simpler shapes, consisting of disks with three disjoint caps. Comparison results for harmonic functions help establish that in non-equilateral configurations the shape derivative has an appropriate sign, contradicting optimality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07708 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shape optimization under width constraint: the Cheeger constant and the torsional rigidity Bogosel, Beniamin Optimization and Control Metric Geometry In this article it is shown that the equilateral triangle maximizes the Cheeger constant and minimizes the torsional rigidity among shapes having a fixed minimal width. The proof techniques use direct comparisons with simpler shapes, consisting of disks with three disjoint caps. Comparison results for harmonic functions help establish that in non-equilateral configurations the shape derivative has an appropriate sign, contradicting optimality. |
| title | Shape optimization under width constraint: the Cheeger constant and the torsional rigidity |
| topic | Optimization and Control Metric Geometry |
| url | https://arxiv.org/abs/2506.07708 |