On a conjecture of Almgren II: area-minimizing submanifolds with fractal singular sets on almost any manifold
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918266953269248 |
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| author | Liu, Zhenhua |
| author_facet | Liu, Zhenhua |
| contents | This paper is the second in a two-part solution to Almgren's conjecture on the existence of area-minimizing submanifolds with fractal singular sets. In part one, we construct area-minimizing submanifolds with fractal singular sets on certain special manifolds. Here we continue our work and show that area-minimizing submanifolds with fractal singular sets exist on almost any smooth manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24859 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a conjecture of Almgren II: area-minimizing submanifolds with fractal singular sets on almost any manifold Liu, Zhenhua Differential Geometry This paper is the second in a two-part solution to Almgren's conjecture on the existence of area-minimizing submanifolds with fractal singular sets. In part one, we construct area-minimizing submanifolds with fractal singular sets on certain special manifolds. Here we continue our work and show that area-minimizing submanifolds with fractal singular sets exist on almost any smooth manifold. |
| title | On a conjecture of Almgren II: area-minimizing submanifolds with fractal singular sets on almost any manifold |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2512.24859 |