JulieNew paper for the end of the year. We found a convex domain in hyperbolic space for which the fundamental gap for Dirichlet eigenvalues of the Laplacian-with-a-convex-potential is NOT minimised by a constant potential. Joint work with Hien Nguyen and Frieder Jaeckel. We were motivated by a similar result for metric graphs. #maths #eigenvalues https://arxiv.org/abs/2512.17103
Constant potentials do not minimise the fundamental gap on convex domains in hyperbolic space
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 $-Î+V$ is strictly smaller than the fundamental gap of $-Î$. In comparison to previous work, this result requires more refined control of the eigenfunctions.
Statistics Globe
Dr. Peter Ranzinger
Victoria Stuart đšđŠ đłïžââ§ïž
Phil Solimine 
jprbarry
Gnash_Equilibrium
Ben Golub 
David Bindel
David Bindel