Minkowski content estimates for generic area minimizing hypersurfaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915785302081536 |
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| author | Li, Xuanyu |
| author_facet | Li, Xuanyu |
| contents | Let $Γ$ be a smooth, closed, oriented, $(n-1)$-dimensional submanifold of $\mathbb{R}^{n+1}$. It was shown by Chodosh-Mantoulidis-Schulze that one can perturb $Γ$ to a nearby $Γ'$ such that all minimizing currents with boundary $Γ'$ are smooth away from a set with Hausdorff dimension less than $n-9$. We prove that the perturbation can be made such that the singular set of the minimizing current with boundary $Γ'$ has Minkowski dimension less than $n-9$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02950 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Minkowski content estimates for generic area minimizing hypersurfaces Li, Xuanyu Differential Geometry Let $Γ$ be a smooth, closed, oriented, $(n-1)$-dimensional submanifold of $\mathbb{R}^{n+1}$. It was shown by Chodosh-Mantoulidis-Schulze that one can perturb $Γ$ to a nearby $Γ'$ such that all minimizing currents with boundary $Γ'$ are smooth away from a set with Hausdorff dimension less than $n-9$. We prove that the perturbation can be made such that the singular set of the minimizing current with boundary $Γ'$ has Minkowski dimension less than $n-9$. |
| title | Minkowski content estimates for generic area minimizing hypersurfaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2312.02950 |