Connectedness properties of small minimal clusters in Riemannian or Finsler manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915265758887936 |
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| author | Nardulli, Stefano Pratelli, Aldo |
| author_facet | Nardulli, Stefano Pratelli, Aldo |
| contents | We prove that in a compact Riemannian manifold, the $m$-minimal clusters of sufficiently small total volume are connected and with small diameter, while in a more general Finsler manifold they are done by at most $m$ connected components of small diameter. We apply these results to calculate the asymptotic expansion of the multi-isoperimetric profile at the first nontrivial order, for small volumes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20587 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Connectedness properties of small minimal clusters in Riemannian or Finsler manifolds Nardulli, Stefano Pratelli, Aldo Functional Analysis Differential Geometry We prove that in a compact Riemannian manifold, the $m$-minimal clusters of sufficiently small total volume are connected and with small diameter, while in a more general Finsler manifold they are done by at most $m$ connected components of small diameter. We apply these results to calculate the asymptotic expansion of the multi-isoperimetric profile at the first nontrivial order, for small volumes. |
| title | Connectedness properties of small minimal clusters in Riemannian or Finsler manifolds |
| topic | Functional Analysis Differential Geometry |
| url | https://arxiv.org/abs/2504.20587 |