Calibration for minimal surfaces with free boundary and Cheeger-type problems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918187046535168 |
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| author | Bouchitté, Guy Phan, Minh |
| author_facet | Bouchitté, Guy Phan, Minh |
| contents | We study a problem of minimal surfaces with free boundary written in the form of a non convex minimization problem. Our aim is to characterize optimal solutions by finding a suitable calibration field. A natural upper bound of the infimum is given by a variant of the Cheeger problem that we solve explicitly proving the optimality thanks to the construction of a cut-locus potential. The comparison with the original problem is then discussed in detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03322 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Calibration for minimal surfaces with free boundary and Cheeger-type problems Bouchitté, Guy Phan, Minh Analysis of PDEs Optimization and Control 49J45, 49N15, 49Q10, 65K10, 90C26 We study a problem of minimal surfaces with free boundary written in the form of a non convex minimization problem. Our aim is to characterize optimal solutions by finding a suitable calibration field. A natural upper bound of the infimum is given by a variant of the Cheeger problem that we solve explicitly proving the optimality thanks to the construction of a cut-locus potential. The comparison with the original problem is then discussed in detail. |
| title | Calibration for minimal surfaces with free boundary and Cheeger-type problems |
| topic | Analysis of PDEs Optimization and Control 49J45, 49N15, 49Q10, 65K10, 90C26 |
| url | https://arxiv.org/abs/2511.03322 |