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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.12621 |
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| _version_ | 1866910002877300736 |
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| author | Li, Haizhong Yang, Bo |
| author_facet | Li, Haizhong Yang, Bo |
| contents | In Euclidean space $\mathbb{R}^n$, the minimization problem of a nonlocal isoperimetric functional with a competition between perimeter and a nonlocal term derived from the negative power of the distance function, has been extensively studied. In this paper, we investigate this nonlocal isoperimetric problem in hyperbolic space $\mathbb{H}^n$, we prove that the geodesic balls are unique minimizers (up to hyperbolic isometries) for small volumes $m$ and obtain nonexistence results for large volumes $m$ under certain ranges of the exponent in the nonlocal term. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_12621 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and nonexistence results for a nonlocal isoperimetric problem on $\mathbb{H}^n$ Li, Haizhong Yang, Bo Analysis of PDEs Mathematical Physics Differential Geometry 49Q10, 49Q20, 81V35 In Euclidean space $\mathbb{R}^n$, the minimization problem of a nonlocal isoperimetric functional with a competition between perimeter and a nonlocal term derived from the negative power of the distance function, has been extensively studied. In this paper, we investigate this nonlocal isoperimetric problem in hyperbolic space $\mathbb{H}^n$, we prove that the geodesic balls are unique minimizers (up to hyperbolic isometries) for small volumes $m$ and obtain nonexistence results for large volumes $m$ under certain ranges of the exponent in the nonlocal term. |
| title | Existence and nonexistence results for a nonlocal isoperimetric problem on $\mathbb{H}^n$ |
| topic | Analysis of PDEs Mathematical Physics Differential Geometry 49Q10, 49Q20, 81V35 |
| url | https://arxiv.org/abs/2512.12621 |