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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/2512.15403 |
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| _version_ | 1866911324316893184 |
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| author | Milman, Emanuel Neeman, Joe |
| author_facet | Milman, Emanuel Neeman, Joe |
| contents | We verify that an isoperimetric minimizing cluster on a simply connected homogeneous Riemannian manifold with at most one end always has connected boundary. In particular, the boundary of a single-bubble isoperimetric minimizer on such manifolds must be connected, and hence all isoperimetric sets and their complements must be connected. This is demonstrably false without the simple connectedness assumption or the restriction on the number of ends. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15403 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the connectedness of a minimizing cluster's boundary Milman, Emanuel Neeman, Joe Differential Geometry Geometric Topology We verify that an isoperimetric minimizing cluster on a simply connected homogeneous Riemannian manifold with at most one end always has connected boundary. In particular, the boundary of a single-bubble isoperimetric minimizer on such manifolds must be connected, and hence all isoperimetric sets and their complements must be connected. This is demonstrably false without the simple connectedness assumption or the restriction on the number of ends. |
| title | On the connectedness of a minimizing cluster's boundary |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2512.15403 |