Optimal smooth approximation of integral cycles
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913586488541184 |
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| author | Almgren, Fredrick Browder, William Caldini, Gianmarco De Lellis, Camillo |
| author_facet | Almgren, Fredrick Browder, William Caldini, Gianmarco De Lellis, Camillo |
| contents | In this article we prove that each integral cycle $T$ in an oriented Riemannian manifold $\mathcal{M}$ can be approximated in flat norm by an integral cycle in the same homology class which is a smooth submanifold $Σ$ of nearly the same area, up to a singular set of codimension 5. Moreover, if the homology class $τ$ is representable by a smooth submanifold, then $Σ$ can be chosen free of singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17678 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal smooth approximation of integral cycles Almgren, Fredrick Browder, William Caldini, Gianmarco De Lellis, Camillo Differential Geometry Analysis of PDEs In this article we prove that each integral cycle $T$ in an oriented Riemannian manifold $\mathcal{M}$ can be approximated in flat norm by an integral cycle in the same homology class which is a smooth submanifold $Σ$ of nearly the same area, up to a singular set of codimension 5. Moreover, if the homology class $τ$ is representable by a smooth submanifold, then $Σ$ can be chosen free of singularities. |
| title | Optimal smooth approximation of integral cycles |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2411.17678 |