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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.02299 |
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| _version_ | 1866917033629712384 |
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| author | Dimler, Bryan Lee, Chen-Kuan |
| author_facet | Dimler, Bryan Lee, Chen-Kuan |
| contents | We show that every compactly supported smoothly calibrated integral current with connected $C^{3,α}$ boundary is the unique solution to the oriented Plateau problem for its boundary data. The same holds true for compactly supported $``$continuously calibrated$"$ integral flat chains. This is proved as a consequence of the boundary regularity theory for area-minimizing currents and a unique continuation argument in the spirit of Frank Morgan. In codimension one, the argument yields a sufficient condition for uniqueness in the oriented Plateau problem expressed in terms of the regularity of the calibrating form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02299 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniqueness in the Plateau problem for calibrated currents Dimler, Bryan Lee, Chen-Kuan Differential Geometry Analysis of PDEs 49Q15 We show that every compactly supported smoothly calibrated integral current with connected $C^{3,α}$ boundary is the unique solution to the oriented Plateau problem for its boundary data. The same holds true for compactly supported $``$continuously calibrated$"$ integral flat chains. This is proved as a consequence of the boundary regularity theory for area-minimizing currents and a unique continuation argument in the spirit of Frank Morgan. In codimension one, the argument yields a sufficient condition for uniqueness in the oriented Plateau problem expressed in terms of the regularity of the calibrating form. |
| title | Uniqueness in the Plateau problem for calibrated currents |
| topic | Differential Geometry Analysis of PDEs 49Q15 |
| url | https://arxiv.org/abs/2510.02299 |