Generic regularity for minimizing hypersurfaces in dimension 11
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915345979146240 |
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| author | Chodosh, Otis Mantoulidis, Christos Schulze, Felix Wang, Zhihan |
| author_facet | Chodosh, Otis Mantoulidis, Christos Schulze, Felix Wang, Zhihan |
| contents | We prove that area-minimizing hypersurfaces are generically smooth in ambient dimension $11$ in the context of the Plateau problem and of area minimization in integral homology. For higher ambient dimensions, $n+1 \geq 12$, we prove in the same two contexts that area-minimizing hypersurfaces have at most an $n-10-ε_n$ dimensional singular set after an arbitrarily $C^\infty$-small perturbation of the Plateau boundary or the ambient Riemannian metric, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generic regularity for minimizing hypersurfaces in dimension 11 Chodosh, Otis Mantoulidis, Christos Schulze, Felix Wang, Zhihan Differential Geometry Analysis of PDEs We prove that area-minimizing hypersurfaces are generically smooth in ambient dimension $11$ in the context of the Plateau problem and of area minimization in integral homology. For higher ambient dimensions, $n+1 \geq 12$, we prove in the same two contexts that area-minimizing hypersurfaces have at most an $n-10-ε_n$ dimensional singular set after an arbitrarily $C^\infty$-small perturbation of the Plateau boundary or the ambient Riemannian metric, respectively. |
| title | Generic regularity for minimizing hypersurfaces in dimension 11 |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2506.12852 |