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

Julie Clutterbuck, Frieder Jäckel, Xuan Hien Nguyen

We show that for every $n\ge 2$ 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…