Density of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913485777010688 |
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| author | Nardulli, Stefano Resende, Reinaldo |
| author_facet | Nardulli, Stefano Resende, Reinaldo |
| contents | In the present work, we consider area minimizing currents in the general setting of arbitrary codimension and arbitrary boundary multiplicity. We study the boundary regularity of 2d area minimizing currents, beyond that, several results are stated in the more general context of $(C_0, α_0, r_0)$-almost area minimizing currents of arbitrary dimension $m$ and arbitrary codimension taking the boundary with arbitrary multiplicity. Furthermore, we do not consider any type of convex barrier assumption on the boundary, in our main regularity result which states that the regular set, which includes one-sided and two-sided points, of any 2d area minimizing current $T$ is an open dense set in the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_11947 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Density of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity Nardulli, Stefano Resende, Reinaldo Analysis of PDEs 49Q15, 49Q05, 53A10, 49Q20 In the present work, we consider area minimizing currents in the general setting of arbitrary codimension and arbitrary boundary multiplicity. We study the boundary regularity of 2d area minimizing currents, beyond that, several results are stated in the more general context of $(C_0, α_0, r_0)$-almost area minimizing currents of arbitrary dimension $m$ and arbitrary codimension taking the boundary with arbitrary multiplicity. Furthermore, we do not consider any type of convex barrier assumption on the boundary, in our main regularity result which states that the regular set, which includes one-sided and two-sided points, of any 2d area minimizing current $T$ is an open dense set in the boundary. |
| title | Density of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity |
| topic | Analysis of PDEs 49Q15, 49Q05, 53A10, 49Q20 |
| url | https://arxiv.org/abs/2204.11947 |