Constant potentials do not minimise the fundamental gap on convex domains in hyperbolic space
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911327448989696 |
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| author | Clutterbuck, Julie Jäckel, Frieder Nguyen, Xuan Hien |
| author_facet | Clutterbuck, Julie Jäckel, Frieder Nguyen, Xuan Hien |
| contents | We show that for every $n \geq 2$ and $D > 0$ there exist a convex domain $Ω\subseteq \mathbb H^n$ with diameter $D$ and a convex potential $V$ on $Ω$ such that the fundamental gap of the operator $-Δ+V$ is strictly smaller than the fundamental gap of $-Δ$. In comparison to previous work, this result requires more refined control of the eigenfunctions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_17103 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constant potentials do not minimise the fundamental gap on convex domains in hyperbolic space Clutterbuck, Julie Jäckel, Frieder Nguyen, Xuan Hien Analysis of PDEs Differential Geometry 35P15, 49R05, 58C40 We show that for every $n \geq 2$ and $D > 0$ there exist a convex domain $Ω\subseteq \mathbb H^n$ with diameter $D$ and a convex potential $V$ on $Ω$ such that the fundamental gap of the operator $-Δ+V$ is strictly smaller than the fundamental gap of $-Δ$. In comparison to previous work, this result requires more refined control of the eigenfunctions. |
| title | Constant potentials do not minimise the fundamental gap on convex domains in hyperbolic space |
| topic | Analysis of PDEs Differential Geometry 35P15, 49R05, 58C40 |
| url | https://arxiv.org/abs/2512.17103 |