On a conjecture of Almgren: area-minimizing submanifolds with fractal singularities
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866918182633078784 |
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| author | Liu, Zhenhua |
| author_facet | Liu, Zhenhua |
| contents | We construct area-minimizing submanifolds with fractal singular sets on compact Riemannian manifolds. Thus, we settle a conjecture by Almgren and our answer is sharp dimensionwise. Furthermore, we can prescribe arbitrarily the strata in the Almgren stratification of the singular sets of our area-minimizing submanifolds, and our results hold in the category of integral currents, mod v currents and stable stationary varifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_13137 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On a conjecture of Almgren: area-minimizing submanifolds with fractal singularities Liu, Zhenhua Differential Geometry We construct area-minimizing submanifolds with fractal singular sets on compact Riemannian manifolds. Thus, we settle a conjecture by Almgren and our answer is sharp dimensionwise. Furthermore, we can prescribe arbitrarily the strata in the Almgren stratification of the singular sets of our area-minimizing submanifolds, and our results hold in the category of integral currents, mod v currents and stable stationary varifolds. |
| title | On a conjecture of Almgren: area-minimizing submanifolds with fractal singularities |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2110.13137 |