Preprint
Jul 2026
Log-Concavity and Level-Set Horoconvexity of the First Eigenfunction on Horoconvex Domains in the Hyperbolic Plane
Let $\Omega\subset\mathbb H^2$ be a bounded smooth horoconvex domain and let $\psi_1>0$ be its first Dirichlet eigenfunction. We prove that \[ \operatorname{Hess}_{\mathbb H^2}(-\log\psi_1)>0 \] throughout $\Omega$, with no restriction on the diameter or the first eigenvalue. The proof is by contradiction. A degenerate...
Xianzhe Dai, John M. Ennis, X. H. Nguyen et al.
· 0 citations