The Fine Structure of the Singular Set of Area-Minimizing Integral Currents III: Frequency 1 Flat Singular Points and $\mathcal{H}^{m-2}$-a.e. Uniqueness of Tangent Cones
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914724114857984 |
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| author | De Lellis, Camillo Minter, Paul Skorobogatova, Anna |
| author_facet | De Lellis, Camillo Minter, Paul Skorobogatova, Anna |
| contents | We consider an area-minimizing integral current $T$ of codimension higher than 1 ins a smooth Riemannian manifold $Σ$. We prove that $T$ has a unique tangent cone, which is a superposition of planes, at $\mathcal{H}^{m-2}$-a.e. point in its support. In combination with works of the first and third authors, we conclude that the singular set of $T$ is countably $(m-2)$-rectifiable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_11553 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Fine Structure of the Singular Set of Area-Minimizing Integral Currents III: Frequency 1 Flat Singular Points and $\mathcal{H}^{m-2}$-a.e. Uniqueness of Tangent Cones De Lellis, Camillo Minter, Paul Skorobogatova, Anna Analysis of PDEs Differential Geometry 49Q15, 49Q05, 49N60, 35B65, 35J47 We consider an area-minimizing integral current $T$ of codimension higher than 1 ins a smooth Riemannian manifold $Σ$. We prove that $T$ has a unique tangent cone, which is a superposition of planes, at $\mathcal{H}^{m-2}$-a.e. point in its support. In combination with works of the first and third authors, we conclude that the singular set of $T$ is countably $(m-2)$-rectifiable. |
| title | The Fine Structure of the Singular Set of Area-Minimizing Integral Currents III: Frequency 1 Flat Singular Points and $\mathcal{H}^{m-2}$-a.e. Uniqueness of Tangent Cones |
| topic | Analysis of PDEs Differential Geometry 49Q15, 49Q05, 49N60, 35B65, 35J47 |
| url | https://arxiv.org/abs/2304.11553 |