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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.07877 |
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| _version_ | 1866910046051368960 |
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| author | Lin, Fanghua Shoshan, Malkeil Wang, Changyou |
| author_facet | Lin, Fanghua Shoshan, Malkeil Wang, Changyou |
| contents | The purpose of this note is to present a positive answer to an open problem proposed in the recent book \cite{Brezis-Mironescu} by H. Brezis and P. Mironescu. It has been stated in this book {\it Sobolev Maps to the Circle} as Proposition 4.3. We demonstrate, in particular, the value of the least mass of the area minimizing integral rectifiable currents with a given boundary equals to the infimum of areas among smoothly immersed submanifolds with the same boundary, under the assumption that the boundary is that of a smooth submanifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07877 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a Problem Posed by Brezis and Mironescu Lin, Fanghua Shoshan, Malkeil Wang, Changyou Analysis of PDEs Differential Geometry 58E12 The purpose of this note is to present a positive answer to an open problem proposed in the recent book \cite{Brezis-Mironescu} by H. Brezis and P. Mironescu. It has been stated in this book {\it Sobolev Maps to the Circle} as Proposition 4.3. We demonstrate, in particular, the value of the least mass of the area minimizing integral rectifiable currents with a given boundary equals to the infimum of areas among smoothly immersed submanifolds with the same boundary, under the assumption that the boundary is that of a smooth submanifold. |
| title | On a Problem Posed by Brezis and Mironescu |
| topic | Analysis of PDEs Differential Geometry 58E12 |
| url | https://arxiv.org/abs/2603.07877 |