A nonlocal approximation of the area in codimension two
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910867745931264 |
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| author | Caselli, Michele Freguglia, Mattia Picenni, Nicola |
| author_facet | Caselli, Michele Freguglia, Mattia Picenni, Nicola |
| contents | For $s\in (0,1)$ we introduce a notion of fractional $s$-mass on $(n-2)$-dimensional closed, orientable surfaces in $\R^n$. Moreover, we prove its $Γ$-convergence, with respect to the flat topology, and pointwise convergence to the $(n-2)$-dimensional area. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13696 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A nonlocal approximation of the area in codimension two Caselli, Michele Freguglia, Mattia Picenni, Nicola Differential Geometry Analysis of PDEs Optimization and Control 49J45, 28A75, 49Q20 For $s\in (0,1)$ we introduce a notion of fractional $s$-mass on $(n-2)$-dimensional closed, orientable surfaces in $\R^n$. Moreover, we prove its $Γ$-convergence, with respect to the flat topology, and pointwise convergence to the $(n-2)$-dimensional area. |
| title | A nonlocal approximation of the area in codimension two |
| topic | Differential Geometry Analysis of PDEs Optimization and Control 49J45, 28A75, 49Q20 |
| url | https://arxiv.org/abs/2406.13696 |