$C^\infty$ rectifiability of stationary varifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910853724372992 |
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| author | Brena, Camillo De Lellis, Camillo Franceschini, Federico |
| author_facet | Brena, Camillo De Lellis, Camillo Franceschini, Federico |
| contents | In this paper we prove that, for every integers $m\geq 2$ and $n\geq 1$, the support of any stationary $m$-dimensional integer rectifiable varifold $V$ in an open set $U\subset \mathbb R^{m+n}$ is $C^\infty$ rectifiable, namely it can be covered, up to an $H^m$-null set, with countably many $C^\infty$ $m$-dimensional graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_00649 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $C^\infty$ rectifiability of stationary varifolds Brena, Camillo De Lellis, Camillo Franceschini, Federico Analysis of PDEs Differential Geometry In this paper we prove that, for every integers $m\geq 2$ and $n\geq 1$, the support of any stationary $m$-dimensional integer rectifiable varifold $V$ in an open set $U\subset \mathbb R^{m+n}$ is $C^\infty$ rectifiable, namely it can be covered, up to an $H^m$-null set, with countably many $C^\infty$ $m$-dimensional graphs. |
| title | $C^\infty$ rectifiability of stationary varifolds |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2503.00649 |