An existence theorem for sliding minimal sets
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918155025121280 |
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| author | David, Guy Labourie, Camille |
| author_facet | David, Guy Labourie, Camille |
| contents | We prove an existence theorem for the sliding boundary variant of the Plateau problem for $2$-dimensional sets in $\mathbb{R}^n$. The simplest case of sufficient condition is when $n=3$ and the boundary $Γ$ is a finite disjoint union of smooth closed curves contained in the boundary of a convex body, but the main point of our sufficient condition is to prevent the limits in measure of a minimizing sequence to have singularities of type $\mathbb{Y}$ along $Γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01905 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An existence theorem for sliding minimal sets David, Guy Labourie, Camille Classical Analysis and ODEs 49K99, 49Q20 We prove an existence theorem for the sliding boundary variant of the Plateau problem for $2$-dimensional sets in $\mathbb{R}^n$. The simplest case of sufficient condition is when $n=3$ and the boundary $Γ$ is a finite disjoint union of smooth closed curves contained in the boundary of a convex body, but the main point of our sufficient condition is to prevent the limits in measure of a minimizing sequence to have singularities of type $\mathbb{Y}$ along $Γ$. |
| title | An existence theorem for sliding minimal sets |
| topic | Classical Analysis and ODEs 49K99, 49Q20 |
| url | https://arxiv.org/abs/2510.01905 |