Existence and nonexistence results for a nonlocal isoperimetric problem on $\mathbb{H}^n$

Haizhong Li; Bo Yang

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arXiv · 2512.12621

Existence and nonexistence results for a nonlocal isoperimetric problem on $\mathbb{H}^n$

Haizhong Li·Bo Yang

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Abstract

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.

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BibTeX RIS

Haizhong Li, Bo Yang. 2025-12-14. Existence and nonexistence results for a nonlocal isoperimetric problem on $\mathbb{H}^n$. https://arxiv.org/abs/2512.12621

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