Isoperimetric Regions in Anisotropically Scaled Product Manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909954621833216 |
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| author | Vernadakis, Efstratios |
| author_facet | Vernadakis, Efstratios |
| contents | Let $M, N$ be compact Riemannian manifolds. Then, for fixed volume fraction, in the product of a sufficiently small homothetic copy of $M$ with $N$, every isoperimetric region is the product of $M$ with an isoperimetric region in $N$, provided the boundaries of the isoperimetric regions in $N$ are smooth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09490 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isoperimetric Regions in Anisotropically Scaled Product Manifolds Vernadakis, Efstratios Differential Geometry 49Q10, 49Q20, 53C21, 53C42 Let $M, N$ be compact Riemannian manifolds. Then, for fixed volume fraction, in the product of a sufficiently small homothetic copy of $M$ with $N$, every isoperimetric region is the product of $M$ with an isoperimetric region in $N$, provided the boundaries of the isoperimetric regions in $N$ are smooth. |
| title | Isoperimetric Regions in Anisotropically Scaled Product Manifolds |
| topic | Differential Geometry 49Q10, 49Q20, 53C21, 53C42 |
| url | https://arxiv.org/abs/2512.09490 |