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arXiv · 2512.17103

Constant potentials do not minimise the fundamental gap on convex domains in hyperbolic space

Julie Clutterbuck·Frieder Jäckel·Xuan Hien Nguyen
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Abstract

We show that for every $n \geq 2$ and $D > 0$ there exist a convex domain $\Omega \subseteq \mathbb H^n$ with diameter $D$ and a convex potential $V$ on $\Omega$ such that the fundamental gap of the operator $-\Delta+V$ is strictly smaller than the fundamental gap of $-\Delta$. In comparison to previous work, this result requires more refined control of the eigenfunctions.

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Julie Clutterbuck, Frieder Jäckel, Xuan Hien Nguyen. 2025-12-18. Constant potentials do not minimise the fundamental gap on convex domains in hyperbolic space. https://arxiv.org/abs/2512.17103

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