Area-minimizing submanifolds are not generically smooth
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916801064992768 |
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| author | Liu, Zhenhua |
| author_facet | Liu, Zhenhua |
| contents | We prove that area-minimizing submanifolds are not generically smooth, settling a conjecture of White that asks the generic smoothness of area-minimizing submanifolds. We furthermore establish a lower bound on the Hausdorff dimension of the singular sets of area-minimizing submanifolds with respect to open sets of Riemannian metrics. The lower bound is $\max\{d-5,d-c\},$ where $d$ denotes the dimension of the submanifold and $c$ denotes the codimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_08315 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Area-minimizing submanifolds are not generically smooth Liu, Zhenhua Differential Geometry We prove that area-minimizing submanifolds are not generically smooth, settling a conjecture of White that asks the generic smoothness of area-minimizing submanifolds. We furthermore establish a lower bound on the Hausdorff dimension of the singular sets of area-minimizing submanifolds with respect to open sets of Riemannian metrics. The lower bound is $\max\{d-5,d-c\},$ where $d$ denotes the dimension of the submanifold and $c$ denotes the codimension. |
| title | Area-minimizing submanifolds are not generically smooth |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2206.08315 |