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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.13995 |
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| _version_ | 1866912490732912640 |
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| author | Bronsard, Lia Neumayer, Robin Novack, Michael Skorobogatova, Anna |
| author_facet | Bronsard, Lia Neumayer, Robin Novack, Michael Skorobogatova, Anna |
| contents | We construct partitions of $\mathbb{R}^n$ into three sets $\{\mathscr{X}(1),\mathscr{X}(2),\mathscr{X}(3)\}$ that locally minimize interfacial area among compactly supported volume preserving variations and that blow down at infinity to singular area-minimizing cones. As a consequence, we prove the non-uniqueness of the standard lens cluster in a large number of dimensions starting from $8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13995 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the non-uniqueness of locally minimizing clusters via singular cones Bronsard, Lia Neumayer, Robin Novack, Michael Skorobogatova, Anna Analysis of PDEs We construct partitions of $\mathbb{R}^n$ into three sets $\{\mathscr{X}(1),\mathscr{X}(2),\mathscr{X}(3)\}$ that locally minimize interfacial area among compactly supported volume preserving variations and that blow down at infinity to singular area-minimizing cones. As a consequence, we prove the non-uniqueness of the standard lens cluster in a large number of dimensions starting from $8$. |
| title | On the non-uniqueness of locally minimizing clusters via singular cones |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.13995 |